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MAPPING AND MODELING GLACIAL LAKE ALGONQUIN
IN NORTHERN MICHIGAN AND WESTERN ONTARIO
WITH MODELS OF UNCERTAINTY
by

Scott A. Drzyzga

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree Of

DOCTOR OF PHILOSOPHY
Department of Geography

2007

ABSTRACT

MAPPING AND MODELING GLACIAL LAKE ALGONQUIN
IN NORTHERN MICHIGAN AND WESTERN ONTARIO
WITH MODELS OF UNCERTAINTY
By

Scott A. Drzyzga

This dissertation is the first work to map the ”Upper Group" sequence of
glacial Lake Algonquin water planes in northern Michigan and western Ontario.
Position data were collected from relict shoreline features, which were uplifted
during isostatic readjustment after deglaciation. Geostatistical models were built
to describe regional uplift trends and reconstruct the now warped water planes
associated with the Main, Ardtrea, Upper Orillia and Lower Orillia phases. Each
water plane model was used to adjust a digital contemporary elevation model
and create a digital pro-glacial elevation model, which reflected both local
topography and the regional pattern of isostatic depression that existed during
that particular lake phase. Data were subjected to accuracy assessments that
permitted models Of uncertainty about input data errors to be included in each
landscape reconstruction process. Accordingly, each map depicts the extent of a
former lake phase and expresses two components of uncertainty about predicted

paleoshoreline locations: one associated with the precision of the predicted water

plane elevation; and another associated with co-located uncertainty about error
in the digital contemporary elevation model.

Important findings of this work include, but are not limited to: a) Main
phase and lower shorelines found on Cockburn Island, Ontario, suggest the
island was deglaciated before the outlet at North Bay, Ontario was opened; b)
relict features at Beaver Island, Michigan, indicate the Main and Ardtrea phases
extended into the Michigan basin, but data collected near Little Traverse Bay,
Michigan, suggest many ”highest” glacial Lake Algonquin Shorelines in the
Michigan basin do not correlate with the Main phase; and c) similarities between
isobases mapped during this work and recently published isobases that Show
contemporary uplift rates suggest that the regional pattern of isostatic
readjustment have not changed much during the last 11,000 years.

This study also found evidence of convergence between the Main and
Ardtrea water planes, which suggests differential uplift relative to the Fenelon
Falls outlet was the cause of shoreline deformation and tilt during these phases.
This study does not resolve the question, however, Of where glacial Lake

Algonquin stood in the southern parts of the Huron and Michigan basins.

Copyright by
SCOTT A. DRZYZGA
2006

ACKNOWLEDGEMENTS

I owe a special thanks to Ashton Shortridge for accepting the
responsibility of advising me during his first and busy years at Michigan State
University, and for his time and commitment ever Since. Not only has he
encouraged me to think in new ways and supported my professional endeavors,
he has encouraged me to express my opinions in my writing and to not conceal
them behind the curtain Of absolute Objectivity.

I am grateful for each member of my doctoral committee. I thank Randy
Schaetzl for recruiting me into his Seminar in Physical Geography; the
experience truly inspired this work and provided me with valuable
opportunities to publish early in my career. I thank Judy Olson for helping me to
think through many mapping problems; not the least was learning to understand
how map projections and coordinate systems really work. From Iudy, I also
learned the values of knowing your audience and good map design. And, I am
grateful for the many conversations I shared with Alan Arbogast; particularly
one on a hot day at Ludington State Park. We climbed atop a large sand dune
and looked over many others situated between Lake Michigan and Hamlin Lake.
Alan talked about how he could see the landscape evolve in his mind’s eye. He
could see winds, changes in water level, stabilization and destabilization, and

sands burying soils. At the time, I just stood there and wondered because I saw

only sand and junipers. That conversation stuck with me, however, because it let
me realize I needed to ”see” Lake Algonquin as Alan had ”seen” his dunes if I
were to be successful in this work, and for it to be accepted by others. That
moment fully arrived while I, alone on an uninhabited island, was standing on a
relict offshore bar and looking at a relict wave-cut bluff; I could see those ancient
waves break and those waters swash where today no water is present. I see
those waves still and have owned my research ever since.

I thank Dr. Grahame Larson, Of the Department of Geology, for serving as
the Dean of the College of Social Science’s representative at my dissertation
defense. His questions helped me to identify and recognize valuable findings
that I had overlooked. I enjoyed learning from him.

I extend gratitude and thanks to Mr. L. Avra, Of the Huron Timber
Company of Thessalon, Ontario; my work at Cockburn Island would not have
been possible without his permission or the assistance provided to me by his
foreman and crew. I also thank Mr. H. McQuarrie, a retired logger and seasonal
resident of Cockburn Island, who gave me his hand-drafted map Of properties,
logging roads and foot trails. Funding for fieldwork was provided by the
Association Of American Geographers via a Doctoral Dissertation Improvement
Grant, and a Graduate Research Fellowship from the Department of Geography

at Michigan State University.

vi

I extend gratitude and thanks tO Drs. P. F. Karrow, W. R. Cowan and C. F.
M. Lewis, and to Kevin Kincare and Beth Weisenborn, for Sharing data and
insights regarding glacial Lake Algonquin.

I thank Rick and janis Herman, my wonderful cousins, for graciously
providing me a home while I was in Michigan and conducting field work. I will
always remember our morning coffees, and those afternoons when Rick would
help me clear my head with a round of golf and a cold beer.

Last but not least, I thank Cathryn Dowd for supporting me while we
were in Illinois and I was getting my research off the ground, for helping me
return to Michigan to conduct fieldwork, and for putting up with me while we
were in Pennsylvania and I was trying simultaneously to finish my dissertation

and start a new career. I owe a tremendous debt to her.

vii

TABLE OF CONTENTS

LIST OF TABLES ................................................................................ xi
LIST OF FIGURES .............................................................................. xiv
CHAPTER 1: INTRODUCTION ............................................................ 1
Background about glacial Lake Algonquin ........................................ 2
Statement of problem ................................................................... 4
Statement Of purpose and research Objectives .................................... 5
Definitions of key terms ................................................................ 6
Error .................................................................................. 7

Accuracy ............................................................................. 7

Precision ............................................................................. 7
Uncertainty ......................................................................... 8

Elevation ............................................................................ 8

Location ............................................................................. 9

Position .............................................................................. 9
Justification for research ............................................................... 9
Organization Of the dissertation ...................................................... 11
CHAPTER 2: LAKE LEVELS AND SHORELINES .................................... 14
Introduction ............................................................................... 14

A word about shorelines ............................................................... 16
Glacial Lake Algonquin ................................................................ 17
Relict shoreline indicators and water level proxies .............................. 27
Variation in Great Lakes water levels ............................................... 36
Short-term events .................................................................. 38

Cyclic fluctuations ................................................................ 40
Long-term trends .................................................................. 43
Summary ............................................................................ 44
Summary ................................................................................... 46
CHAPTER 3: METHODS AND FIELD CAMPAIGNS ................................ 48
Introduction ............................................................................... 48

The initial glacial Lake Algonquin dataset ........................................ 48
Opportunities to improve the glacial Lake Algonquin dataset ............... 51
Shoreline identification, bluff selection, and sampling methods ............. 53
Data processing ........................................................................... 58
Summary of prior mapping Campaigns ............................................ 61
Mapping campaigns conducted for this work .................................... 64

viii

Cockburn Island, Ontario ....................................................... 67

Sugar Island, Michigan .......................................................... 74
Rexford, Michigan ................................................................ 76

The Munuscong Islands ......................................................... 79
Kincheloe, Michigan .............................................................. 82
Mackinac Island, Michigan ..................................................... 83

The Douglas Lake area, Michigan ............................................. 87
Beaver Island, Michigan ......................................................... 92
From Petoskey to Traverse City, Michigan .................................. 99

The Leelanau Peninsula, Michigan ........................................... 104
From Mullet Lake to Alpena, Michigan ..................................... 108
From Alpena to the Au Sable River, Michigan ............................ 110
From the Au Sable River to Saganing, Michigan .......................... 112
Summary ................................................................................... 116
CHAPTER 4: ACCURACY ASSESSMENTS ............................................. 126
Introduction ............................................................................... 126
Two datasets .............................................................................. 127
Assessment of the glacial Lake Algonquin dataset .............................. 129
Analysis Of potential selection errors ......................................... 130
Ground control ..................................................................... 131
Analysis of measurement errors ............................................... 134
Cumulative elevation errors in paleoshoreline data ..................... 140
Assessment Of the National Elevation Dataset .................................... 142
Geoprocessing the NED ......................................................... 145
Hypsometric analysis ............................................................ 146
Ground control ..................................................................... 150
Select results of the first exploratory analysis .............................. 152
Complete results Of the second exploratory analysis ..................... 157
Covariation with location, elevation, and slope ........................... 164
Spatial autocorrelation ........................................................... 170
Summary ................................................................................... 170
CHAPTER 5: THE SPATIAL MODEL ..................................................... 175
Introduction ............................................................................... 175
Modeling outcomes of a spatial random process ................................ 176
Building the spatial model ............................................................ 187
Models Of elevation errors in the paleoshoreline elevation data ............. 192
Assumed model of selection errors ........................................... 192
Empirical model of measurement errors .................................... 194
Model of cumulative errors ..................................................... 195
Models of differentially upwarped water planes .................................. 197
A note about coordinate transformation ....................................... 201
Main phase ............................................................................ 202

ix

Ardtrea phase ........................................................................ 207

Upper Orillia phase ................................................................. 212
Lower Orillia phase ................................................................. 217
Cedar Point phase ................................................................... 221
Models of errors in the digital elevation model .................................. 223
Variography ........................................................................... 225
Making predictions .................................................................. 230
Running the Spatial model ........................................................ 232
Summary ................................................................................... 236
CHAPTER 6: MAPPING THE RESULTS ................................................. 241
Introduction ............................................................................... 241
Summary of results obtained from the spatial model ........................... 241
Maps of glacial Lake Algonquin shorelines ........................................ 246
The Main phase ...................................................................... 253
The Ardtrea phase .................................................................. 256
The Upper Orillia phase ........................................................... 258
The Lower Orillia phase ........................................................... 260
Maps Of glacial Lake Algonquin Shorelines that reveal uncertainty ........ 261
Composites map Of Main Lake Algonquin and the Upper Group... . .. 264
Summary ................................................................................... 279
CHAPTER 7: CONCLUSIONS .............................................................. 283
Introduction ............................................................................... 283
Re-evaluation of research Objectives ................................................ 284
To find and survey relict shoreline features that best serve as 284

To reconstruct water planes associated with glacial Lake Algonquin 290
To reconstruct the landscape associated with each lake phases and 295
To express the degree of uncertainty with which each glacial Lake 296

Future research ........................................................................... 297
Glacial Lake Algonquin ............................................................ 298
Topographic map analysis ........................................................ 300
Visualizing uncertainty ............................................................ 300
Global climate change and sea-level rise ....................................... 301

Final thoughts ............................................................................. 302

APPENDICES .................................................................................... 297
Appendix A: The glacial Lake Algonquin dataset ............................... 298
Appendix B: Scripts written for use with R ....................................... 317

REFERENCES .................................................................................... 326

LIST OF TABLES

Table 2.1: Glacial Lake Algonquin lake phases with time frames. Lake
phases are listed in descending order in terms of both contemporary

elevation and age. Radiocarbon dates are from Karrow et a1. (1975) ............. 25
Table 2.2: Seasonal variation in contemporary Great Lakes water levels

(Quinn, 2002; NOAA, 2006) .................................................................. 37
Table 2.3: Potential range of Great Lakes water-level fluctuations (see text

for references) .................................................................................... 45
Table 3.1: Approximate elevations for glacial Lake Algonquin water planes

and the Nipissing water plane at Sault Ste. Marie and Manitoulin Island,

Ontario (Cowan, 1985) ......................................................................... 62
Table 3.2: Lake level elevations for glacial Lake Algonquin water planes and

the Nipissing water plane at the southern end of protO-St. Joseph Island,

Ontario (Karrow, 1987) ........................................................................ 63
Table 3.3: Approximate elevations Of glacial Lake Algonquin water planes at
Cockburn Island, Ontario .................................................................... 72
Table 3.4: Approximate elevations of glacial Lake Algonquin water planes

and the Nipissing water plane measured in western Chippewa County ........ 78
Table 3.5: Approximate elevations of glacial Lake Algonquin water planes
measured in the Munuscong Islands region ............................................. 82
Table 3.6: Approximate elevations Of glacial Lake Algonquin water planes
measured at Mackinac Island, Michigan .................................................. 87
Table 3.7: Approximate elevations of glacial Lake Algonquin water planes

and the Nipissing water plane measured in the Douglas Lake area ............... 91
Table 3.8: Approximate elevations of glacial Lake Algonquin water planes
measured at Beaver Island, Michigan ...................................................... 99
Table 4.1: Vertical differences between measured and published heights.

N GS bench marks are indicated by their Permanent Identifiers (PIDS) ........... 133

xi

Table 4.2: Summary statistics that describe the set of differences between
measured and published bench mark elevations ....................................... 135

Table 4.3: Results Of Kendall’s non-parametric tests for associations between
position and elevation error .................................................................. 139

Table 4.4: Horizontal differences between measured and published NGS
benchmark locations ........................................................................... 140

Table 4.5: Summary statistics that describe differences between actual and
co-located elevations in the original and corrected DEM surfaces ................. 154

Table 4.6: Summary statistics that describe differences between actual and
co-located DEM elevations ................................................................... 159

Table 4.7: Results Of two-sample difference-Of-means tests among DEM
subsets ............................................................................................. 163

Table 4.8: Results of Kendall’s tests for association between easy-tO-measure
landscape variables and: a) signed error and b) unsigned error .................... 166

Table 5.1: Main phase trend parameters estimated via ordinary least squares. 203

Table 5.2: Summary Of Main surface residuals Obtained via ordinary least
squares (OLS), cross-validated universal kriging with a nugget model only
(CV.NUG), and cross-validated universal kriging with a Matern model Of

spatial structure (CV.MAT) .................................................................. 203

Table 5.3: Ardtrea phase trend parameters estimated via ordinary least
squares (OLS), and generalized least squares (GLS) ................................... 209

Table 5.4: Summary statistics for residuals (n=41) Obtained from Ardtrea
water plane models predicted via ordinary least squares (OLS), generalized
least squares (GLS), and cross-validated universal kriging (CV.NUG) ........... 210

Table 5.5: Upper Orillia phase trend parameters estimated via ordinary least
squares ............................................................................................. 214

Table 5.6: Summary statistics for residuals (n=33) Obtained from Upper

Orillia elevation trend models obtained via ordinary least squares (OLS),
cross-validated universal kriging with pure nugget model (CV.NUG) and
cross-validated universal kriging with anisotropic covariance model

(CV .MAT) ........................................................................................ 214

xii

Table 5.7: Lower Orillia phase trend model parameters estimated via
ordinary least squares (OLS), and generalized least squares (GLS) ............... 218

Table 5.8: Summary statistics for residuals (n=16) Obtained from Lower

Orillia water plane models predicted via ordinary least squares (OLS),
generalized least squares (GLS) and cross-validated universal kriging

(CV .UK) ........................................................................................... 219

Table 5.9: Cedar Point phase trend parameters estimated via ordinary least
squares (OLS) .................................................................................... 222

Table 6.1: Estimates of total land area under water during each lake phase.
Percentages of contemporary land area under water are indicated in
parentheses ....................................................................................... 246

Table A1: The glacial Lake Algonquin datatset ......................................... 298

xiii

LIST OF FIGURES

Figure 1.1: The extents of glacial Lake Algonquin hypothesized by Hough
(1958) and Larsen (1987) ...................................................................... 3

Figure 2.1: Terms used to describe morphologic features along the beach
profile (adapted from Komar, 1998) ....................................................... 15

Figure 2.2: Baedke et al. (2004) used buried foreshore deposits as shoreline
indicators. Figure adapted from descriptions in their text and from Figure
2.6 in Johnston (2004) .......................................................................... 32

Figure 2.3: Schaetzl et al. (2002) used bouldery/ gravelly lags at the bases of
wave-cut bluffs as Shoreline indicators. Figure was adapted from their
Figure 2b (p.405) ................................................................................ 34

Figure 3.1: The study area explored by Schaetzl et a1. (2002), points in the

original glacial Lake Algonquin dataset, and the extent of the Main phase of
glacial Lake Algonquin as they had determined it. Figure adapted from their
Figure 1 ............................................................................................ 50

Figure 3.2: Map of the current study area with names Of places and features
mentioned in the text. County boundaries and names added for
reference ......................................................................................... 52

Figure 3.3: Schaetzl et a1. (2002) used bouldery/ gravelly lags at the bases of
wave-cut bluffs as shoreline indicators. Figure was adapted from their
Figure 2b (p.405) ................................................................................ 54

Figure 3.4: Index map for smaller-scaled maps that show field campaigns
and field sites mentioned in this chapter ................................................ 66

Figure 3.5: Relict bluff sites at Cockburn Island, Ontario. Sites are labeled
with a unique site identification number and an elevation value (e. g., 642:
200 m) ............................................................................................. 68

Figure 3.6: Image of a relict bluff on the south side of McCaigs Hill,
Cockburn Island, Ontario .................................................................... 70

Figure 3.7: Diagram of the relict bluff shown in Figure 3.6. Shoreline
positions were measured at gravel lag situated at the base Of the bluff .......... 70

xiv

Figure 3.8: Apparent contours across the Main Lake Algonquin water plane. 73

Figure 3.9: Relict bluff sites at Sugar Island, Michigan. Sites are labeled with
a unique site identification number and an elevation value (e. g., 642: 200 m).
Also shown are the locations of features surveyed by Cowan (1985) ............. 75

Figure 3.10: Relict bluff sites near Rexford, Michigan. Sites are labeled with
a unique site identification number and an elevation value (e. g., 642: 200 m).. 77

Figure 3.11: Relict bluff sites in the Munuscong Islands region. Sites are
labeled with a unique site identification number and an elevation value (e. g.,
642: 200 m) ....................................................................................... 81

Figure 3.12: Relict bluff sites at Mackinac Island. Sites are labeled with a
unique Site identification number and an elevation value (e.g., 642: 200 m). . .. 85

Figure 3.13: Relict bluff sites in the Douglas Lake area. Sites are labeled with
a unique site identification number and an elevation value (e. g., 642: 200 m)... 90

Figure 3.14: Relict bluff sites on Beaver Island, Michigan. Sites are labeled
with a unique site identification number and an elevation value (e. g., 642:
200 m) ............................................................................................. 94

Figure 3.15: Exposed sediment profile in a gravel pit located near the
southern end of protO-Beaver Island. A 2-foot carpenter's level is shown for
scale ................................................................................................ 98

Figure 3.16: Relict bluff sites near Petoskey, Michigan. Sites are labeled with
a unique site identification number and an elevation value (e.g., 642: 200 m)... 100

Figure 3.17: Relict bluff sites on the Leelanau Peninsula. Sites are labeled
with a unique site identification number and an elevation value (e. g., 642:
200 m) ............................................ 103

Figure 3.18: Relict bluff sites in the Black Lake area. Sites are labeled with a
unique site identification number and an elevation value (e. g., 642: 200 m). . .. 108

Figure 3.19: Relict bluff sites in the Long Lake area. Sites are labeled with a
unique site identification number and an elevation value (e. g., 642: 200 m). . .. 109

Figure 3.20: Relict bluff sites near Alpena, Michigan. Sites are labeled with a
unique site identification number and an elevation value (e.g., 642: 200 m). . . .. 111

XV

Figure 3.21: Relict bluff sites in near Harrisville, Michigan. Sites are labeled
with a unique site identification number and an elevation value (e. g., 642:
200 m) ............................................................................................. 112

Figure 3.22: Relict bluff sites in near Oscoda, Michigan. Sites are labeled
with a unique site identification number and an elevation value (e.g., 642:
200 m) ............................................................................................. 114

Figure 4.1: Distribution of error in sampled bench mark elevations: a) Stern
and leaf plot - solid line denotes the decimal place; and b) q-q plot of
standardized errors with a one-to-one line and 90% confidence envelope ...... 135

Figure 4.2: Scatterplots of Signed error in sampled bench mark elevations
and position. Errors and elevations are reported in meters. Latitude and
Longitude values are reported in decimal degrees .................................... 137

Figure 4.3: Scatterplots of unsigned error in sampled bench mark elevations
and position. Errors and elevations are reported in meters. Latitude and
Longitude values are reported in decimal degrees .................................... 138

Figure 4.4: Frequency histograms of elevation. Bin width is one meter .......... 148

Figure 4.5: Histograms of: a) 529 check point elevations; and b) all DEM
elevations in the study area. The difference between frequency scales is the
results of unequal sample sizes ............................................................. 152

Figure 4.6: Scatterplots Of DEM-reported and actual elevations for the (a)
original DEM and for (b) the corrected DEM ............................................ 153

Figure 4.7: Scatterplots of DEM error and the linear components Of slope
aspect .............................................................................................. 155

Figure 4.8: Map of DEM errors at control point locations. The map reveals
no global pattern but suggests error values exhibit some spatial continuity at

short distances. The image is presented in color ........................................ 158
Figure 4.9: Histograms of elevation errors in the DEM .............................. 160
Figure 4.10: Q-Q plots of standardized elevation errors in the DEM ............. 161

Figure 4.11: Scatterplots of: a) signed error and slope gradient; and b)
unsigned error and slope gradient. Black lines drawn to emphasize zero
error ................................................................................................ 169

xvi

Figure 4.12: Map and scatterplot of ground control locations used to assess
error in the Ontario subset ................................................................... 169

Figure 5.1: The spatial model Schaetzl et a1. (2002) used to reconstruct
landscapes in northern Michigan associated with glacial Lake Algonquin. . . 188

Figure 5.2: The spatial model used in this work to digitally reconstruct water
planes and landscapes in northern Michigan and western Ontario that were
associated with glacial Lake Algonquin. The model was run 100 times for

each water plane, which produced a set of 100 results that were summarized

to reveal the influences of input data errors ............................................. 191

Figure 5.3: Histograms of errors generated randomly. Error values are
binned in 0.25 m intervals .................................................................... 195

Figure 5.4: Histogram of cumulative paleoshoreline elevation errors. Error
values are binned in 0.25 m intervals. Frequency scale is different than that
used in Figure 5.2 ............................................................................... 197

Figure 5.5: Empirical variograms of Main trend surface residuals generated
via ordinary least squares. Solid lines represent fitted variogram models ...... 205

Figure 5.6: The Main Algonquin water plane: a) predicted elevations are
contoured with a 10-meter interval; and b) greater uncertainties are
expressed with darker gray tones. Sample sites are shown as black dots ....... 207

Figure 5.7: Empirical variogram model fitted to the Spatial structure of
Ardtrea water plane residuals generated during ordinary least squares. . . . . . 210

Figure 5.8: The Ardtrea phase water plane: a) predicted elevations are
contoured with a 10-meter interval; and b) greater uncertainties are
expressed with darker gray tones. Sample Sites are shown as black dots ....... 211

Figure 5.9: Spatial structure of residuals Obtained during attempts to model
the Upper Orillia water plane via ordinary least squares ............................ 215

Figure 5.10: The Upper Orillia phase water plane: a) predicted elevations are
contoured with a 10-meter interval; and b) greater prediction uncertainties
are expressed with darker gray tones. Sample sites are shown as black dots... 217

Figure 5.11: Spatial structure of 01.5 residuals generated during attempts to
model the Lower Orillia water plane ...................................................... 219

xvii

Figure 5.12: The Lower Orillia phase water plane: a) predicted elevations are
contoured with a 10-meter interval; and b) greater prediction uncertainties
are expressed with darker gray tones. Sample sites are shown as black dots... 221

Figure 5.13: Empirical semi-variograms and variogram models for DEM
subsets ............................................................................................. 227

Figure 5.14: Composite surface of predicted DEM errors. The image in this
dissertation is presented in color ............................................................ 231

Figure 5.15: Uncertainty in the surface of predicted DEM errors. Darker

tones are associated with larger confidence intervals and hence greater
uncertainties. Areas Shown in white were masked from analysis to facilitate
computation ..................................................................................... 232

Figure 5.16: Composite surfaces Of DEM errors. Cells shown in gray were
masked from analysis to facilitate computation, but later set to zero. The
image in this dissertation is presented in color .......................................... 234

Figure 5.17: Contemporary uplift rates (cm / century) derived from the ICE-
3G geophysical model (Tushingham and Peltier, 1991). Figure adapted from
Tushingham (1992: 445) ....................................................................... 238

Figure 5.18: Contemporary uplift rates (cm/ century) derived from historical
lake gauge data. Figure adapted from Mainville and Craymer (2005: 1077). 239

Figure 6.1: Predicted shorelines of the Main phase Of glacial Lake Algonquin
in the study area. Shorelines are represented as blackened areas; greater
widths imply greater uncertainty about shoreline location .......................... 248

Figure 6.2: Predicted shorelines of the Ardtrea phase Of glacial Lake
Algonquin in the study area. Shorelines are represented as blackened areas;
greater widths imply greater uncertainty about shoreline location ................ 249

Figure 6.3: Predicted shorelines of the Upper Orillia phase of glacial Lake
Algonquin in the study area. Shorelines are represented as blackened areas;
greater widths imply greater uncertainty about shoreline location ................ 250

Figure 6.4: Predicted shorelines of the Lower Orillia phase of glacial Lake
Algonquin in the study area. Shorelines are represented as blackened areas;
greater widths imply greater uncertainty about shoreline location ................ 251

xviii

Figure 6.5: The Main phase Of glacial Lake Algonquin. Darker tones
indicated greater uncertainties about the predicted water plane. The image
in this dissertation is presented in color ................................................ 265

Figure 6.6: The Ardtrea phase of glacial Lake Algonquin. Darker tones
indicated greater uncertainties about the predicted water plane. The image in
this dissertation is presented in color ..................................................... 266

Figure 6.7: The Upper Orillia phase of glacial Lake Algonquin. Darker tones
indicated greater uncertainties about the predicted water plane. The image in
this dissertation is presented in color ..................................................... 267

Figure 6.8: The Lower Orillia phase Of glacial Lake Algonquin. Darker tones
indicated greater uncertainties about the predicted water plane. The image in
this dissertation is presented in color ..................................................... 267

Figure 6.9: The Main (dark gray), Ardtrea (pink), Upper Orillia (purple), and
Lower Orillia (green) phases Of Lake Algonquin. The image in this
dissertation is presented in color ............................................................ 269

Figure 6.10: Areas on Cockburn Island that were predicted to be above
glacial Lake Algonquin water levels. The extent of this figure corresponds
with the extent of Figure 3.5. The image in this dissertation is in color .......... 270

Figure 6.11: Areas in the Munuscong Island region that were predicted to be
above glacial Lake Algonquin water levels. The extent Of this figure

corresponds with the extent of Figure 3.11. The image in this dissertation is

in color ............................................................................................. 271

Figure 6.12: Areas in the Douglas Lake area that were predicted to be above
glacial Lake Algonquin water levels. This extent of this figure corresponds

with the extent of Figure 3.13. The image in this dissertation is presented in

color ................................................................................................ 272

Figure 6.13: Areas near Charlevoix that were predicted to be above glacial
Lake Algonquin water levels. This extent Of this figure corresponds with the
extent Of Figure 3.16. The image in this dissertation is presented in color ...... 274

Figure 6.14: Areas south of Alpena, Michigan, predicted to be above glacial
Lake Algonquin water levels. This extent of this figure corresponds with the
extent Of Figure 3.20. The image in this dissertation is presented in color ...... 275

xix

Figure 6.15: Areas near Oscoda, Michigan, predicted to be above glacial Lake
Algonquin water levels. This extent Of this figure corresponds with the

extent of Figure 3.22. The apparent line west Of Oscoda marks the southern

limit of the study area. The image in this dissertation is presented in color. . .. 276

Figure 6.16. The Rapid River outvvash fan/ delta during the: a) Main; b)

Ardtrea; c) Upper Orillia; and d) Lower Orillia phases. Pictured is a portion

of the USGS 1:24,000 Torch River 7.5 Minute Series Quadrangle, but rescaled

to 1:63,500 for display. Darkened areas are predicted to have been under

water at with 90% confidence. The image in this dissertation is presented in
color .............................................................................................. 277

Figure 6.17. Pullup Lake and the surrounding area during the : a) Main; b)
Ardtrea; c) Upper Orillia; and d) Lower Orillia phases. Pictured is a

composite of the USGS 1:24,000 Gilchrist and Roberts Corner 7.5 Minute

Series Quadrangles, but rescaled to 1:63,500 for display. Darkened areas are
predicted to have been under water with 90% confidence. The image in this
dissertation is presented in color ............................................................ 278

XX

CHAPTER 1: INTRODUCTION

This dissertation reports research about reconstructing and visualizing a
sequence of pro-glacial lakes that existed in the Great Lakes basin more than
10,000 years ago. The sequence, known as glacial Lake Algonquin, cannot be
Observed directly, but its existence is inferred from relict Shoreline features
perched above contemporary lake levels.

The tasks of mapping relict Shoreline features and drawing lines on maps
to reconnect them are made difficult by several factors: some features exhibit
evidence Of many water levels while others exhibit evidence of only one; long
distances separate many relict features; and the earth’s surface has been
differentially lifted and tilted in the Great Lakes region, so different features
created along the perimeter Of the same water surface might no longer be
situated along the same plane of elevation. Accordingly, there is some confusion
in the literature regarding the numbers of water levels and lake phases that
existed, and which shoreline features belong to which lake phase (Schaetzl et al.,
2002). This work enlists the power Of computers and geostatistical methods to
explore and analyze paleoshoreline data, to build and test spatial models of
differential uplift and tilt, and to reconstruct some of these ancient landscapes.

This research is much more than reconnecting Old bits of Shorelines; it is
about working with imperfect data and dealing with uncertainties that propagate

through spatial models and into results. Moreover, Shorelines are not static like

the lines drawn on maps to represent them. They are dynamic over multiple
spatial and temporal scales. This research attempts to describe completely what
is known and knowable about shoreline locations. Ultimately, this work
develops a new way Of looking at the land-water interface and Offers a stochastic
representation --- a fundamental breakthrough in the way shorelines can be

visualized.

Brief background about glacial Lake Algonquin

Glacial Lake Algonquin was a sequence of pro-glacial lakes in the Great
Lakes basin (Figure 1.1). It maintained relative high water levels from 11,200 to
10,400 yr BP 1 (see Figure 12 in Karrow, 1975) and developed conspicuous
shoreline features (Larson and Schaetzl, 2001). As the Laurentide glacier receded
from the basin, lower outlets were uncovered and lake levels fell in stages
(Larson and Schaetzl, 2001). The land surface rebounded upward as the weight
of the ice was removed; the adjustment process is called isostatic rebound.
Locations in northern Michigan and Ontario, which are closer to the former
centers of ice loading, have rebounded at rates faster than locations in southern
Michigan (The Coordinating Committee on Great Lakes Basic Hydraulic and
Hydrologic Data, 1977, 2001). Consequently, landforms associated with the

sequence have become differentially lifted and tilted.

 

1 Conventional radiocarbon ages are reported in years before present (yr BP).

The datum, 0 yr BP, corresponds tO calendar year 1950 AD.

 

 

«4‘ _ Approximate ice-
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State or province

  
           

Extent of Lake Algonquin

 

 

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Figure 1.1: The extents of glacial Lake Algonquin hypothesized by Hough (1958)
and Larsen (1987).

Much has been written about how glacial Lake Algonquin was formed
(Spencer, 1891; Gilbert, 1898; Goldthwait, 1908; Leverett and Taylor, 1915; and
Stanley, 1936), but little agreement exists about the elevations and spatial extents
of its water surfaces (Hough, 1958; Futyma, 1981; Larsen, 1987; and see Figure
1.1). Little agreement exists because the earth’s surface has been lifted and tilted
over the past 10,000 years and many relict landforms have been altered by
natural and human processes; some were buried or reworked by later lake
transgressions. Uncertainty about the timing and extents of this lake sequence

prompted an extensive survey by Schaetzl et a1. (2002). The authors employed

global positioning technology to measure positions along relict Lake Algonquin
features. They used a GIS and a digital elevation model to analyze their
paleoshoreline dataset and interpolate unknown shoreline locations. In brief,
they used a GIS to model the cumulative effects of the isostatic rebound process

over space and estimate the spatial extents of several water surfaces.

Statement of problem

Spatial data quality is a theme that has ebbed and flowed through the
course of literature devoted to Geographic Information Systems (GIS) and
Geographic Information Science (GISc). Yet, it seems many people are
indifferent to this line of work because the same warnings have been issued time
and time again. For example, Goodchild and Gopal (1989) claimed virtually all
spatial datasets stored in a GIS are, to some extent, contaminated by error.
Thirteen years later, Heuvelink and Burrough repeated the same message: ”data
stored in a spatial database are rarely, if ever, truly free of error” (Heuvelink and
Burrough, 2002: 111).

Burrough (1992) once baited the spatial modeling community to include
assessments of spatial data quality and error propagation as ingredients of
intelligent spatial model design. The community at large did not take the bait
and Heuvelink (1998) was compelled to reiterate the dangers in work that
utilizes GIS yet fails to assess errors inherent in the data sets used or propagated

through the spatial models employed. Together, Heuvelink and Burrough (2002)

have argued it is crucial ” to know how accurate the data contained in spatial
databases really are" (p.111), because without that knowledge neither the true
value of the information derived, nor the correctness of the decisions they
support can be evaluated.

Assessing spatial data quality and decontaminating spatial datasets are
difficult and often tedious and frustrating tasks for in most cases only imperfect
knowledge exists about the amount of error contained in any one observation, let
alone among any set of observations. Data errors, inaccuracies, or imprecision,
even when acknowledged, are often absorbed into analyses; their impacts on
results left unexamined and potential consequences ignored. A need exists to
demonstrate the value of assessing spatial data quality and uncertainty
propagation in work that utilizes GIS. Perhaps Motro summarized this need best

when he wrote:

Uncertainty permeates our understanding of the real world. The
purpose of information systems is to model the real world. Hence
information systems must be able to deal with uncertainty (Motro,

1993, cited in Parsons, 1996: 2).

Statement of purpose and research objectives
The purpose of this research is to demonstrate the value of assessing
spatial data quality, incorporating information and uncertainty about input data

errors into spatial model design, and visualizing uncertainties propagated

through work accomplished within a GIS environment. To achieve this end, this
work reconstructs the paleolandscapes of glacial Lake Algonquin, and shows by
example how accuracy assessments, uncertainty models, and visualizations of
uncertainty can be used to aide and improve such an undertaking. Accordingly,
this research has the following objectives:
1. To find and survey relict shoreline features that best serve as indicators of
former lake levels;
2. To conflate new paleoshoreline data with data collected during previous
mapping campaigns;
3. To reconstruct water planes associated with the various phases of glacial
Lake Algonquin;
4. To reconstruct the landscape associated with each lake phase and map the
distribution of shorelines;
5. And, to express the degree of uncertainty with which each shoreline

location has been mapped.

Definitions of key terms
Many data quality concepts are commonly, but erroneously, used inter-
changeably. This work relies heavily on several of these concepts, so I offer

definitions for them below.

Error

Error is the difference between an attribute value and its measured
representation. All measured values contain error because the precisions of
human ability and equipment are finite. The term error includes not only
mistakes, bias, and blunders, but the statistical concept of variation.
Accuracy

Accuracy refers to the quality of a measurement and indicates whether or
not it contains an acceptable amount of error. A measurement is accurate if it
contains an acceptable amount of error (or less); it is inaccurate if it contains
more. Although accuracy can be considered a binary condition (i.e., being one of
only two possible states), it is used more commonly to refer to the degree of
conformity between measured and true values (Wolf and Dewitt, 2000). Such
use permits the accuracy of one measurement to be compared to the accuracy of
another in relative terms (e. g., measurement x is more accurate than
measurement y).
Precision

Precision refers to the quality of a measurement process and is commonly
used to indicate the exactness of values obtained by that process. According to
Wolf and Dewitt (2000), precision can be assessed by taking repeated
measurements of a single quantity and examining the variance. The process, and
the exactness of values obtained from it, is considered imprecise if the variance
exceeds a predetermined threshold. The process, and the exactness of values

7

obtained from it, is considered precise if repeated measurements vary less than
the threshold.
Uncertainty

Western science idealizes prefect data and information because they
support rational thought and quick decisions, but uncertainty lurks as an
intrinsic property of many concepts, ideas, and data (Couclelis, 2003). According
to MacEachren (2005: 140), ” when inaccuracy is known objectively, it can be
expressed as error; when it is not known, the term uncertainty applies.” Yet,
there is no generally agreed-upon definition of uncertainty, so it is most often
treated as a multi-faceted characterization that embodies related concepts
including error, accuracy, precision, validity, variability, noise, fuzziness,
vagueness, completeness, and reliability (Buttenfield, 1993; Pang, 2001;
MacEachren, 2005). I use the term to connote the degree of confidence with
which something can be known given available data or information. According
to Christakos (2000), determinations and reports of uncertainty are the hallmarks
of geostatistical analysis and important to processes related to risk assessment
and decision-making.

This research also relies heavily on the terms elevation, location and
position. I define them below.
Elevation

Elevation is a 1-dimensional measure of vertical distance, or height. All
elevations in this work are referenced to the WGS84 ellipsoid and GEOID03

8

geoid models, which are used to specify the familiar concept of mean sea level in
and around the United States.
Location

Location refers to a 2-dimensional measure of horizontal distances
between a point and the origin of a coordinate system. The system can be
geographic, in which case locations are specified with pairs of longitude and
latitude values. All geographic coordinates in this work are referenced to the
WG584 and NAD83 geographic coordinate systems, which are used
interchangeably. The system can be planar, in which case locations are expressed
as pairs of easting and northing values. Unless noted otherwise, all planar
coordinates are referenced to the Michigan GEOREF planar coordinate system.
Position

Position refers to a 3-dimensional specification of a point in space and

includes specifications of both elevation and location (see above).

Justification for research

This research continues the exploration and mapping traditions of
Geographic research and offers new and original contributions. For example,
this work offers the first known maps of the Upper Orillia and Lower Orillia
shorelines (Deane, 1950) of glacial Lake Algonquin. And, this work offers the
first reported survey of relict shoreline features at Cockburn Island, Ontario.

Other contributions are incremental because they build upon the

geomorphologic research and data collection activities initiated more than a
century ago by Spencer (1891), Lawson (1891), and others. For example, this
research expands upon the work of Schaetzl et al. (2002) and Drzyzga et al. (2002)
by offering updated reinterpretations of extant paleoshoreline data, updated
water plane reconstructions, and maps of Lake Algonquin shorelines that cover a
geographic area broader than they had studied. New data points also fill some
of the large data gaps that Cowan (1985) had mentioned; there be fewer dragons
on the map now (Blake, 1999).

This research also provides the field of Geography with a fundamental
contribution - a new way of looking at the land-water interface. A stochastic
representation of a shoreline embodies variation in water levels and, hence, the
degree of confidence with which the location of a shoreline, as it is traditionally
conceptualized, can be known. While the application of this new method is
limited in this research to the reconstruction of ancient lakes in the Great Lake
basin, it can also be applied to other paleolimnologic reconstructions and
adapted for use in contemporary applications that focus on riparian and coastal
land use issues.

This research is intrinsically geographic because it synthesizes concepts,
knowledge, and tools from multiple disciplines to study a portion of the Earth. It
employs methods developed in the field of Geographic Information Science to
address a long-standing physiographic and paleolimnologic problem. Some

geomorphologists might find issue with the lack of stratigraphy or rheology in

10

this work, for example, and geostatisticians will not find any new theories here,
just applications of existing methods. But, it is the synthesis and novel
application of ideas borrowed from multiple disciplines to address a long-
standing problem that forms the basis of my contribution.

As an aside, the idea of large pro-glacial lakes and icy waters washing
over vast areas of land we now call Ontario or Michigan is both fascinating and
unnerving because it forces the mind to visualize a landscape unlike any that can
be seen on earth. It prompts consideration of a landscape with large glaciers and
without anthropogenic modifications; a cold, wet, windy, and dangerous place.
Yet, glacial Lake Algonquin has inherent value beyond prompting the
imagination in such wild ways -- it places the contemporary Great Lakes system
into a context of landform evolution. Knowing glacial Lake Algonquin existed
reminds us that the Great Lakes have evolved through a history of greater great

lakes and are evolving still.

Organization of the dissertation

The work reported here follows two interleaved threads of research: the
first thread is associated with Objectives 1 and 2 and focuses on my efforts to
find, survey, and correlate relict shoreline features with known glacial Lake
Algonquin lake phases; the second thread is associated with satisfying Objectives
3, 4 and 5 and focuses on my efforts to digitally reconstruct glacial Lake

Algonquin water planes and landscapes, and to estimate the degree of

11

uncertainty with which interpolated shorelines have been mapped. Because each
thread provides a context for examining the other, some reviews of literature,
descriptions of methods, and reports of results are arranged in a noncontiguous
way.

This dissertation is organized into seven chapters. As is traditional, the
first chapter, this one, identifies the scope of the research (i.e., background
materials, the research problem, research questions, and the context and
justification for the work). Chapter 2 reviews the known history of glacial Lake
Algonquin and provides a discussion that recognizes uncertainty as an intrinsic
property of lake levels and shorelines. I also make a case for incorporating the
dynamic nature of shorelines into a study of ancient lakes. Chapter 3 describes
methods used and field campaigns conducted to collect data about Lake
Algonquin lake phases. I document the methods used survey, process, and
classify paleoshoreline data. Because Objectives 1 and 2 needed to be satisfied
before work on Objects 3, 4 and 5 could begin, correlations among collected
paleoshoreline data and Lake Algonquin lake phases are also reported in
Chapter 3. It just made sense to report relict shoreline features and their
correlations with lake phases in one place rather than force the reader to
mentally dovetail multiple landform descriptions and lake phase correlations
that, if reported in the traditional way, would have spanned multiple chapters.
Readers familiar with the seminal work of Leverett and Taylor (1915) will

recognize my attempt to describe fieldwork, features, and correlations as they

12

had done. The narrative style of writing is less formal than I use in other
chapters, but it lends itself to others who might use the text as a field guide
during future research. Chapter 4 offers a comprehensive assessment of the
principal datasets I employ in my analysis: the glacial Lake Algonquin dataset
and a digital elevation model. Relevant literature and methods for assessing the
accuracy of these data are also presented. Chapter 5 presents the crux of the
work. I report work to build uncertainty models that accommodate errors in my
datasets, build geostatistical models of four differentially upwarped water
planes, and incorporate all of this information into a spatial model that predicts
whether or not locations in the area of interest were above or below each water
plane. Relevant literature is also reviewed. Chapter 6 delivers the results; maps
that illustrate paleoshorelines associated with the Main and ”Upper Group”
phases of glacial Lake Algonquin, as well as areas where the locations of these
shorelines remain uncertain. Figure 6.10 is a large-format map that shows the
locations of data points in the glacial Lake Algonquin dataset as well as the
predicted shoreline locations for the entire Upper Group sequence of water
levels. Chapter 7 summarizes the work and identifies goals worth pursuing in
future research. Finally, Appendix A lists every record in the glacial Lake
Algonquin dataset as well as every record in the supplemental database that

holds surveyed features that were retained for future analysis.

13

CHAPTER 2: LAKE LEVELS AND SHORELINES

Introduction

This chapter provides a context for surveying, mapping, and modeling a
sequence of differentially-uplifted water planes associated with glacial Lake
Algonquin. I begin the chapter by introducing glacial Lake Algonquin‘and
providing an abridged history of processes and events that lead to its formation,
lake-level changes through time, and demise. Next, I review work that employs
coastal landforms as shoreline indicators and uses measurements taken from
these landforms as proxies for former water levels. Special attention is given to
the pioneering work of Lawson (1891), who established a precedent for mapping
glacial Lake Algonquin features and correlating sequences stranded at different
locations. Last, I offer a discussion of variation in contemporary Great Lakes
water levels, which is used to infer variation in glacial Lake Algonquin water
levels. The discussion serves two purposes: (1) to estimate the precision with
which an average water level can be measured by taking a spot measurement
from a relict shoreline feature, and (2) to estimate the precision with which two
successive lake phases can be discriminated on the basis of such measurements.

I adopted Komar’s (1976, 1998) nomenclature for describing shorezone
morphology (Figure 2.1). Larsen (1994) employed Komar’s system of names in
his work about glacial Lake Algonquin, so it seems reasonable to continue using

it. Readers are referred to Komar’s latest text (1998) for complete definitions.

14

V

 

littoral zone

 

17

-— offshore+ a inshore foreshore *s— backshore —+‘

 
 
   

 

 

If berms -\

beach I ' b'Ufi

 

 

  

 

    

I
beach-//
scarp

 

longshore bar

Figure 2.1: Terms used to describe morphologic features along the beach profile
(adapted from Komar, 1998).

The landforms illustrated in Figure 2.1 are based on a discrete model of
geographic space. A continuous zone of the earth’s surface is partitioned into
discrete conceptual entities (e. g., longshore bar, beach face, berm, or bluff)
according to sets of relative geomorphometric (e. g., slope aspect, gradient,
curvature), spatial (e. g., landward of a, or seaward of b) or sedimentologic
characteristics (e. g., parent material, grain size). Discrete conceptual entities can
be represented by cartographic objects (i.e., points, lines, and areas) and located
with respect to a known spatial reference system. Digital forms of mapped
objects can be attributed, stored, edited, manipulated, queried, analyzed and

displayed within a GIS environment.

15

A word about shorelines

A shoreline is a conceptual entity that generalizes a dynamic intersection
among bodies of air, land, and water into a simple geometric construct. The
word shoreline connotes an infinitely thin line along the shore, and thus a high-
degree of precision, which lends itself to efficient representation in a visually

manageable form. This connotation is evident in Komar’s (1998) definition:

”Shoreline: The line of demarcation between the water and the

exposed beach. The water’s edge.” (p.47).

In one sense, Komar’s definition is useful because it reduces a complex
phenomenon to an object that can be discussed and analyzed; it facilitates
scientific inquiry and efficient representation on maps or within a GIS
environment. The problem with the definition, however, is that practitioners do
not always agree on how to identify a shoreline in the field (Graham et al., 2003),
and when they do, it is nonetheless difficult to identify and measure consistently
(Parker, 2003).

This research recognizes that a line object is an imprecise representation of
a shoreline because it fails to capture intrinsic variations inherent to the dynamic
air, land, and water interface over the long term. Shorelines move landward as
Water levels rise, and they move lakeward as water levels fall. The more gentle
the beach slope, the greater the horizontal movement. Shorelines do not move

horizontally only when beach slope is infinite (i.e., a vertical cliff or wall). This

16

research attempts to mitigate this imprecision problem by employing a

representation that captures the range of locations (i.e., the area) over which
interface movements occur given variability in water levels. Extant research
about contemporary and historic Great Lakes water-level fluctuations can be
used to condition an expectation about variability in glacial Lake Algonquin

water levels.

Glacial Lake Algonquin

Much of what is known today about glacial Lake Algonquin, its
shorelines, and its water levels was established at the turn of the twentieth
century on the basis of pioneering land surveys and geomorphic reconnaissance
missions. Spencer (1891a) is credited as the first person to attach the Algonquin
moniker to conspicuous bluff relicts and shoreline strands located ”above the
eastern rim of Lake Huron” (Schaetzl eta1., 2002:399). The work of Leverett and
Taylor (1915), however, is generally considered the first authoritative history of
glacial Lake Algonquin. They integrated a set of previous and disparately
located works conducted by themselves and others (e. g., Lawson, 1891 ; Spencer,
1891a; Leverett, 1897; Taylor, 1894 and 1897) in order to make generalizations
about the glacial and post-glacial history of the Great Lakes region. The authors
report included hypotheses and claims about outlet locations, outlet
Chronologies, correlations among features at disparate field sites, enduring lake

Stages, and general patterns of differential crustal deformation. Extant research

17

(e.g., Farrand and Eschman, 1974; Schaetzl et al., 2002), this work included,
continues to recognize the value of Leverett and Taylor’s (1915) synthesis.

Two major contributions have synthesized and thus improved the
collective understanding of Great Lakes evolution: Hough’s (1958) Geology of the
Great Lakes; and Karrow and Calkin’s (1985) Quaternary Evolution of the Great
Lakes. The later represents a collection of individual works that update the lake-
Ievel and outlet histories in each of the lake basins. More recent works by
Pengelly et al. (1997) and Larson and Schaetzl (2001) offer new summaries of
Great Lakes evolution. Another review is warranted here.

Water basins in the Great Lakes region are largely products of repeated
scouring and erosion as continental glaciers advanced, oscillated, and retreated
during the last 2.4 million years; ice flows tended to follow bedrock valley
systems that existed before glaciation (Larson and Schaetzl, 2001). Many sites in
Michigan and Ontario, as well as others in adjacent states, show geomorphic and
stratigraphic evidence of multiple glaciations. Large morainic systems (e.g., the
Lake Border, Port Huron or Munising morainic systems) mark the limits of
particular glacial advances. The last major glacial advance of the Laurentide ice
sheet began 26 ka, covered the entire watershed, and reached a maximum extent
18 ka (Larson and Schaetzl, 2001). After oscillating at the maximum extent for a
few thousand years, the ice sheet margin retreated northward, ”but that retreat
Was interrupted by several readvances at about 15.5, 13.0, 11.8, and 10.0 ka”

(Larson and Schaetzl, 2001: 537). As the southern margin of the Laurentide ice

18

sheet retreated, large pro-glacial lakes formed in topographic sinks where waters
were impounded by glacial ice to the north and high topography elsewhere.
Relict shoreline features (e. g., wave—cut bluffs, beach ridges, spits, and deltas)
mark the limits of pro- and post-glacial lakes that formed during glacial retreats.
Lake waters were displaced during readvances and shoreline features were
overridden or destroyed by glacial ice. The Laurentide ice sheet withdrew from
the watershed roughly 9000 years ago (Larson and Schaetzl, 2001).

The highest set of relict shoreline features north of Georgian Bay was
identified by Spencer (1891a) as remnants of the earliest knowable lake to occupy
the Lake Huron, Michigan and Superior basins simultaneously (Eschman and
Karrow, 1985; Larsen, 1987). Other highest shoreline features were discovered in
the region and reported to occur at prOgressively lower altitudes from north to
south (Larsen, 1987). Lawson (1891), Taylor (1894, 1895, 1897), Leverett (1913)
and Goldthwait (1908, 1910) surveyed relict shoreline features, made correlations
among features stranded at disparate locations, and mapped former lake extents.
They also reported lower shorelines that marked lower and younger lakes.
According to Leverett and Taylor (1915), the four highest shorelines occurred at
progressively lower elevations until they converged at a point south of Traverse
City, Michigan.

Larsen (1987) described how converging shorelines and spatial patterns of

Shoreline deformation and tilt provided grist for Opposing theories of crustal

movement during the late 18003. Gilbert (1890), for example, believed tilted

19

shorelines in the Great Lakes region bore similarities to tilted shorelines found
elsewhere in Utah and, thus, the earth’s crust in the Great Lakes region had been
depressed by the massive weight of a continental ice sheet during glacial
advance and rebounded as the weight of ice diminished during retreat. Gilbert
(1890) adopted an elastic model of crustal movement; patterns of shoreline
deformation and tilt reflected a continuous process of differential isostatic
adjustment since glaciation. Goldthwait (1908, 1910) adopted an alternative
model -- a rigid model of crustal movement -- that required a stable southern
region and a tectonically active northern region; a hinge line model represented
the boundary between these two regions. Goldthwait (1908) assumed crustal
stability in the southern region allowed the glacial Lake Algonquin shoreline to
remain horizontal while episodic tectonic movements somewhere in the northern
region forced crustal uplift. The hinge metaphor provided an explanation for
how a single shoreline could split into multiple shorelines and diverge with
increasing distance, and it suggested rates of episodic movement increased with
distance from the hinge line. Leverett and Taylor (1915) adopted the hinge line
model for use in their landmark manuscript 1, which, in effect, installed the rigid

model of crustal movement as the proper geologic context for conducting

1 Leverett and Taylor (1915) claimed Lake Algonquin attained its greatest extent before a

”great uplift” (p410) had warped the land.

20

subsequent geomorphic research and interpreting relict shorelines during the
next fifty years (e.g., Stanley, 1936; Deane, 1950; and Hough, 1958).

Not until the 19708 did works like Clarke and Persoage (1970) and the
Coordinating Committee on Great Lakes Basic Hydraulic and Hydrologic Data
(1977) report the entire Great Lakes watershed was undergoing differential
vertical movements associated with postglacial rebound - and not only those
locations situated north of a supposed hinge. The spatial isostatic adjustment
pattern was smooth, continuous, and tended to increase from southwest to
northeast and towards the former centers of ice loading. Locations along the
southern shore of Lake Michigan were adjusting at slower rates than locations
near the Port Huron outlet - but adjusting nonetheless. The Coordinating
Committee published a second report (Coordinating Committee, 2001)
confirming the process was ongoing and noting water levels along the southern
shores of the Great Lakes were rising (i.e., transgressing) slowly over time.
Others (e.g., Tushingham, 1992; Clark et al., 1994; Mainville and Craymer, 2005)
have either repeated the experiment or conducted similar work, and all obtained
similar results. These reports debunk Goldthwait’s (1908) rigid earth model.
Kaszycki (1985) and Larsen (1987) have since offered evidence that conflicts with
the hinge line model and suggested glacial Lake Algonquin shorelines plunge
below contemporary lake levels in the supposed southern region.

The glacial readvance of 11.8 ka covered the northern half of the Michigan

basin and the northwestern end of the Huron basin, and it blocked the Straits of

21

Mackinac that, at times, had allowed water to flow from one basin to the other
(Hansel and Mickelson, 1988; Larson and Schaetzl, 2001). Broecker and Farrand
(1963) reported a radiocarbon date (11,850 yr BP) obtained from a forest near
Two Rivers, Wisconsin, that was overridden and buried by this advance. It is
generally believed that pro-glacial Lake Chicago formed in the southern
Michigan basin and drained via an outlet near Chicago, Illinois (Leverett, 1897;
Hansel and Mickelson, 1988), and pro-glacial Lake Algonquin formed in the
southern Huron basin and drained via the Fenelon Falls outlet near Kirkfield,
Ontario (Finamore, 1985; Hansel and Mickelson, 1988). Differential isostatic
rebound changed the relationship between land surface elevations and each field
of equal gravitational potential along which each lake surface rested. For
example, Hansel and Mickelson (1988) reported lake transgression occurred
during the Calumet phase of Lake Chicago as land was uplifted, and Larson and
Schaetzl (2001) reported a contemporaneous lake transgression occurred in the
southern end of the Huron basin as the Fenelon Falls outlet was uplifted at a
faster rate.

As glacial ice retreated from the maximum extent of 11.8. ka, lakes in the
Michigan and Huron basins expanded into sinks formerly occupied by ice. The
lakes were joined when retreating ice uncovered the Indian River lowlands and,
slightly later, the Straits of Mackinac (11,200 yr BP according to Larsen, 1987).
Upon joining, water levels in glacial Lake Chicago dropped to the glacial Lake

Algonquin level (Hansel et al., 1985) and left the outlet at Chicago abandoned

22

(Larson and Schaetzl, 2001). The magnitude of the drop is unknown (Kaszycki,
1985). Continued ice margin retreat allowed glacial Lake Algonquin to enter the
Superior basin (Cowan, 1985; Larson and Schaetzl, 2001). The northern extent of
glacial Lake Algonquin is not known, however, because many shoreline features
in the Superior basin were overridden or destroyed during the next glacial
advance (Cowan, 1985; Farrand and Drexler, 1985).

Differential isostatic rebound continued to change the relationship
between land surface elevations and the field of equal gravitational potential
along which the large surface of glacial Lake Algonquin rested. Eschman and
Karrow (1985: 89) remarked the ”Main Algonquin beach south of the [Fenelon
Falls] outlet represents the maximum of a transgressing water level” whereas
north of the outlet it represents just one of several regressing water levels.
Larson and Schaetzl (2001) noted debate exists regarding whether or not
transgressing waters reached the Port Huron outlet. For example, Pengelly et al.
(1997) insisted that the excavation of the lowest portion of the Niagara Gorge
(between the Erie and Ontario basins) cannot be explained if the Erie basin did
not receive inflow from the Huron basin, but Mothersill and Schurer (2004)
claimed Lake Huron waters bypassed Lake Erie, which allowed extensive plant-
choked swamps to form in Lake Erie’s western sediment basins. In either case, a
combination of continued ice margin retreat and continued uplift ultimately
shifted outflow away from the Fenelon Falls outlet and to the Fossmill outlets

that spilled water into the Ottawa River valley Eschman and Farrand, 1985).

23

The sequence of descending shorelines in the northern Great Lakes region
marks a sequence of progressively younger lake phases. In descending order
(Table 2.1), the sequence is comprised of the highest or Main phase of Lake
Algonquin (Spencer, 1891a; Leverett and Taylor, 1915); an Upper Group
containing the Ardtrea, Upper Orillia and Lower Orillia shorelines / phases that
Deane (1950) identified in Ontario’s Lake Simcoe district; a Lower Group
containing the Wyebridge, Penetang, Cedar Point and Payette shorelines / phases
that Stanley (1936) identified on Ontario’s Penetanguishene Peninsula; and the
very low Sheguiandah and Korah shorelines / phases that Hough (1958)
identified near Sault Ste. Marie, Ontario. Both Karrow (1987) and Larsen (1987)
have noted the controversy that has surrounded these shorelines because it is not
yet known whether glacial Lake Algonquin water levels dropped abruptly as
new outlets were uncovered, or the land surface was differentially lifted above
the field of equal gravitational potential along which the lake surface rested.
Karrow (pers. comm.) recently correlated a sequence of descending outlets with
the sequence of descending lake phases, but his results remain unpublished.
Nevertheless, it seems reasonable to consider that a sequence of discrete short-
term outlet change events occurred during the same period as the continuous
long-term process of isostatic readjustment; the cumulative impacts of both
sequences could produce a very complicated lake-level history.

Glacial Lake Algonquin ended when the North Bay outlet was deglaciated

(Hansel et al., 1985) and the large lake drained leaving three pools: Lake

24

Chippewa in the Michigan basin (Hough, 1955; Hansel et al., 1985; Larson and
Schaetzl, 2001), Lake Stanley in the Huron basin (Hough, 1955; Hansel et al.,
1985; Larson and Schaetzl, 2001), and Lake Hough in the Georgian Bay basin
(Lewis, 1969; Larson and Schaetzl, 2001). Karrow et al. (1975) reported
radiocarbon dates that indicate glacial Lake Algonquin, from the Main phase to
the lowest, existed between 11,200 yr BP and 10,400 yr BP. Individual lake phase

initiations and durations, however, have not yet been dated (Table 2.1).

Table 2.1: Glacial Lake Algonquin lake phases and time frames. Lake phases are
listed in descending order in terms of both contemporary elevation and age.
Radiocarbon dates are from Karrow et al. (1975).

 

Name of lake phase Time frame
The Main phase (Spencer, 1891) 11,200 yr BP - 7
The Upper Group (Deane, 1950)
Ardtrea 7 - 7
Upper Orillia 7 - 7
Lower Orillia 7 - 7

The Lower Group (Stanley, 1936)
Wyebridge
Penetang
Cedar Point
Payette
Sheguiandah (Hough, 1958) . -
Korah (Hough, 1958) ? - 10, 0

v w) w: w: °\J
I I
O w.) -\J 'x) °\) °\J

4:.

yrBP

 

In summary, glacial Lake Algonquin was a sequence of pro-glacial lakes
in the Great Lakes basin (Figure 1.1). It maintained relative high water levels

from 11,200 to 10,400 BP (Karrow et al., 1975; Larson and Schaetzl, 2001). Each

25

water level is assumed to have rested along a field of equal gravitational
potential that can be approximated by a horizontal plane (Clarke et al., 1990).
Assuming the same kinds of erosional and depositional processes that occur
today also occurred during glacial Lake Algonquin times, wave-action at the
perimeter of each lake phase formed shoreline features at or near the horizontal
plane. Observations of stranded sets of descending shoreline features support
the theory that lake levels fell in discrete stages (Lawson, 1891 ; Spencer, 1891b).
The sequence of descending shorelines was attributed to a series of lake phases
(Leverett and Taylor, 1915; Stanley, 1936; Deane, 1950; Hough, 1958).
Observations of tilt among relict shorelines support the theory that water planes,
and hence the entire land surface, were differentially uplifted as the glacier
retreated and the weight of ice diminished (Gilbert, 1898; Schaetzl et al., 2002).
Observations of greater tilt at northern locations and lesser tilt at southern
locations support the theory that the former ice sheet originated in the north and,
after reaching maxima extents, retreated to the north. Observations of greater tilt
rates among higher shorelines and lesser tilt rates among lower shorelines
support the theory that rates of differential uplift have decreased over time
(Larsen, 1987). Together, these theories and the observations that support them
provide an explanation for the origin of the contemporary Great Lakes: they
evolved through a history of greater great lakes. They also provide the basis for

reconstructing glacial Lake Algonquin water planes.

26

Relict shoreline indicators and water level proxies

Lawson’s (1891) study of abandoned shorelines along the north side of
Lake Superior seems to have established a precedent for mapping relict
shorelines and correlating stranded sequences across space. Although Taylor
(18971111) did not agree with many of his interpretations, he did praise ”the high
value of Prof. Lawson’s observations.” Lawson’s data collection methods, as
well as the statements he made about data uncertainty, have particular relevance
to this work about mapping and modeling paleolake levels and shorelines, so
several excerpts are examined below.

Lawson (1891) was interested in the cumulative effects of isostatic
rebound on glacial Lake Algonquin shorelines. His purpose was to ascertain
”what evidences the ancient strand lines of Lake Superior afford of differential
crustal movements” (p.185) and to determine whether or not the ancient strand
lines ”maintained their original horizontality or had been thrown into inclined
altitudes" (p.186). Lawson’s (18912186) objective was to ”secure accurate data as
to the altitude of the various strand lines at as many points as possible and to
gather evidence which would help to trace particular strands around the coast.”

With his purpose and objective in mind Lawson wrote:

[It] was clearly recognized at the outset that it would be hopeless,
owing to the merely local development of shore features, to settle

the question by attempting to trace out continuously any single

27

strand line or any set of such strands. It was, however, believed
that the strands of different vertical series could be correlated,
unless there had been rather complex movements, by carefully

comparing the intervals between them (Lawson, 1891:230-231).

He continued:

In order to effect such a correlation the most accurate possible data
were necessary, and steps were accordingly taken to ascertain the
elevations of the various features indicative of shore lines by

precise engineering methods. (Lawson, 1891:231)

Lawson (1891) was concerned about two types of error in his work: measurement
and selection. The quote above implies concern about the taking of accurate and
precise measurements, yet throughout his work the author voiced confidence
about his team’s ability to conduct an accurate and precise surveyz. Lawson
dwelled considerably, however, on selection error, for he was very concerned
about his ability to interpret relict shorelines consistently and to select points that

indicate former water-levels accurately. He wrote:

The figures [i.e., measured elevations -autlzor’s inclusion] do not

represent always the actual level of the water. The crest of a beach

 

2 Unfortunately, he could not reference his survey to an absolute datum, so no way

exists to assess the absolute accuracy of his measurement technique.

28

is always above the level of the water line at which it is formed; the
rear of a terrace may be sometimes above the actual water line and
occasionally it may be below it, so that in nearly all cases a
correction has to be made for the actual water level. The amount of
this correction is never definitely known so it has been thought best
not to apply it, but to give the figures for the actual observations.

In this connection it is well to note that many of the apparent
discrepancies in strand lines are doubtless due to the varying

value of this correction. (Lawson, 1891:231)

Lawson was concerned about uncertainty. He tried to mitigate uncertainty about
estimating former water plane positions by making observations of modern
beach features encountered at the base of each topographic profile he measured.
For example, Lawson (1891:231) noted, ” the base of a sea-cliff is commonly one
or two feet above the calm water, though occasionally it coincides with the lake-
level closely, and the rear of terraces forming at the mouths of streams is usually
below lake-level." Ultimately, Lawson’s observations lead him to rely primarily
on the bases of stranded sea-cliffs and lake bluffs to be the best shoreline
indicators; elevations taken at the bases to be the best proxies for water levels.
Prompted by debate and uncertainty in the contemporary literature,
Morton and Speed (1998) sought to determine which shore features best serve as

monitors of average water levels and shoreline positions. The authors studied a

29

wave-dominated and micro-tidal environment near Galveston, Texas, and
measured water levels and positions along morphological features on several
sandy beaches. The Great Lakes are considered to be a wave-dominated and
atidal environment, so their findings have some application here.

Morton and Speed (1998) argued random fluctuations in water level
behavior can inhibit the taking of accurate measurements of long-term shoreline
positions, but such fluctuations can be mitigated by using ”a stable beach
feature” (p.1381) as an indicator. They found that, for shores composed of
erodable materials, ” the stability of shoreline features increases landward and
the frequency of movement of a shoreline feature increases seaward” (p.1381).
For example, the toe of a wave-cut bluff is a more stable indicator of shoreline
position than a berm crest or beach ridge along the same shore. The authors also
report discrepancies between measured and actual water levels tend to be
” greatest on low-gradient sandy beaches along a microtidal and wave-
dominated coast”, and, ” in such settings, the mean highest high water line
consistently plots far seaward of the berm crest” (p.1383). Their work
suggests that the average water-level, which by definition is lower in elevation
than the mean highest high water line, also tends to occur far seaward of the

berm crest - likely farther. Given this finding, high-gradient shorezones
COmposed of materials that are less erodable than beach sand (e. g., glacial till,
gravel, or bedrock) may offer better environments for taking accurate

measurements of water levels and shoreline positions than do low-gradient and

30

sandy shorezones. The authors suggest using stable features like erosional bluffs
or scarps, or a vegetation line as indicators. In related work, Moore (2000: p.116
after Morton, 1991) argued that ”where beach morphology permits the
bluff/cliff toe or a vegetation line may be a better choice for shoreline analysis”
than other beach features. The recent findings of Morton and Speed (1998) and
Moore (2000) support the observations and choices that Lawson (1891) made a
century before.

In work on reconstructing late Holocene lake-levels, Thompson (1992) and

others (Baedke et al., 2004; Johnston, 2004; and Thompson and Baedke, 1995;
1997; 1999) focused on sandy depositional features in protected post-glacial
embayments. Relatively coarse foreshore deposits between successive beach
ridges were used as shoreline indicators; elevations taken from them were used
as proxies for water levels (Figure 2.2).

Baedke and Thompson (2004) provided the most recent description of
Thompson’s sampling technique, so I offer a summary of their description here.
A search is made along a horizontal strandplain of beach ridges. Soil and buried

SEdiments are excavated via coring at ” the change in slope that occurs along the
lakeward side of the beach ridge” (Baedke et al., 2004: 440). Core site elevations
are surveyed with sub-centimeter precision. Organic deposits are collected from
the landward swale of the same beach ridge. In a laboratory, cores are analyzed
and summarized in terms of grain size distributions, biological components, and

physical structures. Abrupt and gradational grain-size changes within each

31

vertical core are used to infer the contact between relatively coarse foreshore
deposits and other deposits. The vertical point of contact is assumed to be the
coarsest portion of the horizontal foreshore and related to plunge-point deposits
that occur ”at or very near the still-water elevation of the lake” (Baedke et al.,

2004: 439). 3 Radiocarbon age determinations are made of the organic deposits.

<—Lakeward Landward—’
Beach ridge Beach ridge
crest crest
Swale Swale

 

watertabze

 

Soil co're

contact between coarse foreshore deposits
and other sediments

Figure 2.2: Baedke et al. (2004) used buried foreshore deposits as shoreline
indicators. Figure adapted from descriptions in their text and from Figure 2.6 in
Johnston (2004).

 

3 Neither Thompson (1992) nor Baedke et al. (2004) have offered evidence to suggest the
location of the ”change in slope” on the land surface is an accurate indicator of the

location of the coarsest portion (a.k.a. plunge-point) of a buried foreshore.

Building on Thompson’s early work, Larsen (1994) documented a record
of relative lake-level changes among three locations (Whitefish Point, MI;
Sturgeon Bay, WI; and the Gary Airport, IN) by correlating dated beach ridge
sequences. Like Thompson, Larsen studied beach ridges because they
”preserve continuous geomorphic and stratigraphic records of lake-level change”
(p.108). But unlike Thompson (vis a vis Baedke et al., 2004), Larsen recognized
elevation data taken from buried geomorphic features should be interpreted as
possible outcomes of a fluctuating lake system and not as highly-accurate
sedimentary indicators of statistical mean lake levels (+ / - 0.003 m). Moreover,
Larsen (1994) claimed buried foreshore deposits usually indicate levels within
the upper range of lake levels and, so, not average lake levels. When considered
within the context of the range of contemporary Great Lakes water level
fluctuations (Table 2.2), elevations taken from individual beach ridges could
overestimate average lake-levels by 2.7 meters or more. Larsen’s (1994)
argument was later supported indirectly by Argyilan et al. (2005), who claimed
beach ridges preferentially reflect high water levels.

In work related to this research, Schaetzl et al. (2002) reported concern
about their abilities to identify relict shorelines consistently in the field and to
select points that indicate former water-levels accurately. Like Lawson (1891),
they recognized that different kinds of features, which are formed by different

process, have differing abilities to indicate average paleowater planes

consistently. For example, they reported offshore bars are typically formed

33

below a lake surface whereas a spit crest might rise several meters above it;
elevations taken from these features would underestimate or overestimate
average water levels, respectively. Schaetzl et al. (2002) observed that
postlacustrine debris is often located on the surfaces of benches just below the
bases of wave-cut bluffs and claimed, where present, bouldery/ gravelly lags
provide ”the most credible estimation of mean water level" (p.405). Figure 2.3

illustrates their observation.

 

wave—cut bluff 3///
debris (colluvium & slopewash)

GPS

former mean water level

./ 3" bench bouldery lag

,_... .49.,

wave-built terrace _' -

  

 

 

 

Figure 2.3: Schaetzl et al. (2002) used bouldery/ gravelly lags at the bases of
wave-cut bluffs as shoreline indicators. Figure was adapted from their Figure 2b
(p.405).

Where present, the bouldery/ gravelly lags at the bases of wave-cut bluffs
and the foreshore deposits buried beneath beach ridges have been used

effectively as geomorphic indicators of relict shoreline positions. Both are

34

effective indicators because each consists of relatively coarse—sized sediments
that physically mark the sorting action of swashing and back swashing waters.
Wave-cut bluffs form in erosional environments. Beach ridges form in
depositional environments. In terms of surveying and mapping relict shoreline
features of glacial Lake Algonquin, however, the bouldery/ gravelly lags at the
bases of wave-cut bluffs seem to offer two distinct advantages. First, glacial Lake
Algonquin refers to a sequence of descending lake phases that occurred during a
period of ”strong (hurricane-force) winds” (Krist and Schaetzl, 2001: 11) and
”exceedingly strong waves and currents” (Krist and Schaetzl, 2001: 13), which
suggests wind and wave conditions that favored erosional processes likely
prevailed over gentler conditions that favored depositional processes.
Consequently, I expected erosional landforms associated with Lake Algonquin
shorelines, like wave-cut bluffs, to be more numerous (and easier to find) than
depositional landforms associated with Lake Algonquin shorelines, like
strandplains of beach ridges. And second, for practical purposes, bases of wave-
cut bluffs are more accessible than buried foreshore deposits because wave-cut
bluffs typically do not require trenching or deep coring to reach them in the field.
Therefore, based on the long tradition of glacial Lake Algonquin research,
Lawson's (1891) observations, the recent findings of Morton and Speed (1998)
and Moore (2000), and the related work of Schaetzl et al. (2002), this research
relies on the bouldery/ gravelly lags that form at the bases of wave-cut bluffs to

be the best indicators of glacial Lake Algonquin shorelines. And, using words

35

modified from Lawson (1891), it is understood that measured elevations do not
represent actual water levels, but simply the elevations of shore features ”from
which the actual water levels may be inferred, within certain considerable limits

of error” (Lawson, 1891: 231-232).

Variation in Great Lakes water levels

Contemporary Great Lakes water levels are generally resistant to change
because the bodies of water are deep, have large surface areas, have small
drainage basins relative to lake areas, and are controlled by relatively small
outlets. Under ceteris paribus conditions, the surface of each lake is expected to
rest along a field of equal gravitational potential (Clarke et al., 1990). Yet,
variations in precipitation, air temperature, in-flow, and out-flow force the water
surface to fluctuate and compensate, so lake gauge stations are used to capture,
and statistical techniques are used to summarize, variability in water levels over
time.

The historical water level record provides grist for scientific inquiry.
Quinn (2002), for example, analyzed seasonal variation in the record; Table 2.2
lists average lake levels and portions of Quinn’s summary (Quinn, 2002: Table 1
on page 455). Bishop also (1990) analyzed inter-annual variation and found, ” the
ranges in measured mean monthly levels for Lakes Michigan-Huron and Erie are
approximately 2.4 m and 1.8 m, respectively" (Bishop, 1990: 406). And

Changnon’s (2004) analysis of the lake-level record for Lakes Superior, Michigan-

36

Huron, and Erie found ”record highs or record lows were being set on one or
more lakes during nearly half the time over the 141—year period” (Changnon,
2004: 197). So, although generally resistant, Great Lakes water levels are not

immune to change and change differently over time.

Table 2.2: Seasonal variation in contemporary Great Lakes water levels (Quinn,
2002; NOAA, 2006). 4

 

 

 

Average lake Seasonal Standard
La_k_e level (m a.s.l.) range (m) deviation m1) Time period
Superior 183.5 0.30 0.11 1980-2000
Michigan 176.5 0.27 0.12 1987—2000
Huron 176.5 0.27 0.12 1987-2000
Erie 174.1 0.46 0.15 1861-2000
Ontario 74.6 0.55 0.20 1960-2000

Fluctuations around, or deviations from, long-term average water levels
are generalized into three categories or scales: short-term events (i.e., short time
frames that range from less than one hour to several days and, thus, considered
as events); cycles (i.e., various periods), and long-term trends (i.e., multi-year).
The following sections describe each scale in terms of the contemporary Great
Lakes, and attempt to place them within the context of the relatively large spatial

and temporal domains once occupied by glacial Lake Algonquin. Estimating a

 

4 Quinn (2002) did not report average lake levels, so I estimated average lake levels for a
twenty-year period between January 1, 1980 and January 1, 2000 using NOAA’s Center
for Operational Oceanographic Products and Services data (NOAA, 2006). Data from

the lake gauge situated nearest to each outlet was summarized.

likely range of glacial Lake Algonquin water-level fluctuations is important
because the range can serve as a guiding threshold for discriminating evidences
of different lake surfaces in the field. For example, given a field site with two
instances of a relict coastal landform and a vertical distance between them that is
less than the threshold value, it is reasonable to conclude, based on the observed
difference between elevations alone, that both features were shaped by the same
lake phase operating around the same mean water level. Conversely, given a
field site with two instances of a relict coastal landform but a vertical distance
between them that is greater than the threshold value, it is reasonable to
conclude, based on the difference between elevations alone, that each feature was
shaped by a different lake phase operating around a different mean water level.
Short-term events

Short—term events are the results of differential wind conditions (i.e.,
speed, direction, and fetch) or barometric pressures, which force localized and
temporary imbalances along a water surface. Energy obtained from the
atmosphere is dispersed across the water surface and delivered to the shore in
waves. Wood et al. (1994) studied waves in Lake Michigan and reported most
are one-meter high or less; the maximum observed was approximately six
meters. Gabriel et al. (1997) and Brown et al. (2005) claim storm-generated waves
and seiches can upset water levels by as much as several meters for several
hours. Such short-term events effect local and temporary deviations from, but no

permanent changes to, long-term average water levels.

38

 

When considered in the context of an entire lake surface and over a long
time frame (e.g., decades), chaotic or noisy variations in lake level associated
with all short-term events can be summarized over both space and time.
Accordingly, the large-space and long-term distribution of water-level
fluctuations associated with short-term disturbances on the contemporary Great
Lakes is characterized in this work as the result of an unbiased and unstructured
random process with a zero mean. Although the true variance is unknown, the
quantitative information provided by Wood et al. (1994) suggests the average
deviation is one meter or less.

Storms and storm-generated waves occurred on glacial Lake Algonquin.
Krist and Schaetzl’s (2001) treatment of Lake Algonquin type spits, for example,
provides evidence of coastal erosion and longshore transport processes that were
associated with ”exceedingly strong waves and currents” (p. 13) driven by
”frequent and intense cyclonic storms and their associated wind fields” (p.14).
The modern Great Lakes are not commonly subjected to” strong (hurricane-
force) winds” (p.11) as was glacial Lake Algonquin, so this work infers from
Krist and Schaetzl’s (2001) findings that average and maximum wave heights
were likely greater during glacial Lake Algonquin times than they are today.
The large spatio-temporal distribution of water-level fluctuations associated with
short-term disturbances on glacial Lake Algonquin can be characterized as the
result of an unbiased and unstructured random process with a zero mean and an

average deviation that was at least as great or greater than one meter.

39

Cyclic fluctuations

Lenters (2001) analyzed the historical lake gauge record (from 1860 to
1998) for each Great Lake. His analysis of intra-annual variations revealed the
influences of the annual hydrologic cycle that has been reported by many others
(e.g., Fairchild, 1926; Bishop, 1990; and Angel, 1995). Peak lake levels are
associated with peaks in spring run-off and precipitation, and typically occur in
June (Lakes Huron, Michigan and Superior) or July (Lakes Erie and Ontario);
winter lows, which are associated with precipitation lows, precipitation stored
on land as snow, and evaporation, typically occur in late March or early April.
And, according to Angel (1995), the annual hydrologic cycle generates
fluctuations that range from 20 to 40 cm in any given year.

Lenters’ (2001) analysis of inter-annual variation also revealed changes in
the annual water-level cycle. Each Great Lake has exhibited a trend of
increasing high spring levels and decreasing low autumn levels, although only
trends associated with Lakes Erie and Ontario could be characterized as
statistically significant. Quinn (2002) analyzed water level data for the period
between 1860 and 2000, found similar shifts, and concluded that all of the lakes
have ”experienced changes in their seasonal cycle over the past 140 years”
(Quinn, 2002: 464).

Todd Thompson, by himself (Thompson, 1992) and through work with
others (Thompson et al., 1991; Thompson and Baedke, 1995, 1997 and1999;

Baedke and Thompson, 2000; and Baedke et al., 2004), has developed a research

40

program to investigate periodicity in lake-levels in the upper Great Lakes. The
program is designed to focus not only on historical lake gauge data, but on sandy
depositional features in protected, post-glacial embayments. Thompson searches
the local geologic record for preserved evidence of lake level history. For now,
the longest history observed extends to approximately 4,700 BP. Baedke and
Thompson (2000) identified quasi-periodic lake-level fluctuations that occur at 29
to 38 yr intervals with an average amplitude of 0.5 meters, and a longer-term
fluctuation that occurs over durations between 120 and 180 years and with
average amplitudes between 0.5 and 1.5 meters. More recently, Quinn and
Sellinger (2006) found supporting evidence for such quasi-periodic extreme lake
levels in their analysis of dendrochronologic data, which they linked to
coincident changes in air temperature and precipitation.

The record of glacial Lake Algonquin water level fluctuations is not
known, but it is reasonable to expect that, then, water levels were subject to cyclic
deviations forced by cyclic changes in air temperature or precipitation.
Moreover, glacial Lake Algonquin was bounded to the north by a retreating ice
sheet (Karrow, 1987; Farrand, 1967/ 1998). Fluctuations associated with glacial
discharge and advances or retreats in ice-margin position likely occurred and,
perhaps, were substantial. Tinkler and Pengally (1995) simulated outbursts from
Lake Agassiz into the Upper Great Lakes and found water levels would have
risen between 2 and 20 m; the largest would have required nearly three years for

the Upper Great Lakes to re-attain equilibrium. Disagreement exists, however,

41

about whether or not outflow from Lake Agassiz actually entered the Upper
Great Lakes during Algonquin times (see e. g., the correspondence between
Karrow, 2002 and Teller, 2002). Yet, given the large size of the ice sheet and the
amount of water it probably relinquished during the summer seasons, it is
reasonable to speculate that such variations were greater than, perhaps much
greater than, those contained within the historical lake gauge record, Quinn and
Sellinger’s (2006) tree-ring record, or Baedke and Thompson’s (2000) beach-ridge
record.

Cyclic processes are important catalysts for local coastal erosion processes
(e.g., Loope and Arbogast, 2000; Zurek et al., 2003). When considered in the
global context of the large surface area and the long time frame associated with
glacial Lake Algonquin, variation associated with cyclic processes can be
summarized over space and time. The large spatiotemporal distribution of cyclic
lake—level deviations is characterized in this work as the result of an unbiased
and unstructured random process with a zero mean. Given the quantitative
evidence provided by Lenters (2001) and Baedke and Thompson (2000), and
given the assumption that cyclic water-level fluctuations during glacial Lake
Algonquin times were greater than modern fluctuations, then the range of cyclic
water-level deviations associated with glacial Lake Algonquin lake phases may

easily have exceeded two meters or more.

42

 

 

Long-term trends

Many studies have examined a long-term trend that impacts lake levels,
which is generally thought to be caused by differential vertical movements of the
earth’s crust across the Great Lakes basin (e. g., Coordinating Committee of Great
Lakes Hydraulic and Hydrologic Data, 2001 and 1977; Tushingham, 1992; Clarke
et al., 1994; and Mainville and Craymer, 2005). Quinn and Sellinger (1990)

provide a summary of the process:

”A tremendous weight such as a regional glacier can theoretically
force localized land masses downward into the crust until a
compensatory equilibrium is achieved. Once that weight is
removed, as in a glacial retreat, the landmass will rebound upward
to once again achieve equilibrium. The Laurentide glacier of the
Pleistocene Epoch depressed the crust in the Great Lakes area
differentially because the thickest ice was to the northeast Due to
the varying thicknesses of ice cover over the Great Lakes region,
differential isostatic rebound rates are location specific.” (Quinn

and Sellinger, 1990: 134)

Differential isostatic rebound continues today with land at northern locations
rebounding faster than land at southern locations. Lee and Southam (1994: 409)
report, for example, that land at Michipicoten, Ontario is currently rising 0.525

m/ century faster than land at Duluth, MN, and land at Pt. Iroquois, MI is rising

43

0.122 m/ century with respect to Marquette, MI (from Table 1 on p.410). Ongoing
crustal movement results in differential changes in the relationship between the
land surface that holds water bodies and the fields of gravity that act on the
surfaces of those water bodies. Consequently, isostatic rebound results in
differential changes in the relationship between the elevations of contemporary
shoreline features and relict shoreline features.

Although differential isostatic rebound in the Great Lakes region has been
well studied, little agreement exists about the behavior of the phenomenon, rates
of change in the behavior of the phenomenon since deglaciation, or the amount
of cumulative effect it has had on individual water planes and relict shorelines.
For the purposes of discussion, however, it is important to note that the isostatic
rebound process cannot be characterized as another unbiased and unstructured
random process with a mean of zero; rather, as a spatially structured process
with a non-stationary mean amount of uplift that increases toward the northeast.
Models of isostatic rebound are presented in Chapter 5.

Summary

Apparent random behavior in water-level fluctuations reflects the
superposition of short-term events onto longer-term cyclic processes, which
interact in ways that can produce record highs and lows. In terms of the
contemporary Great Lakes, the cumulative distribution of water-level
fluctuations likely includes deviations from the long-term average that exceed 2.7

meters (see Table 2.3). Quinn (1999) cautions, however, that our understanding

44

of modern lake-level behavior is limited because the current regime may produce
”high and low lake levels with extremes significantly higher than our present

measurements would indicate” (p4).

Table 2.3: Potential range of Great Lakes water-level fluctuations (see text for

 

 

 

references).

Process and duration Typical deviation (m)
Storms or waves

~from seconds to several hours :10
Seasonal hydrologic cycle

~1 year 0.2
Baedke and Thompson (2000)

~33-year cycle 0.5

~150-year cycle 1.0
Differential isostatic rebound

(varies with location) ?

Total i 2.7 m

The range of historic water-level fluctuations is important because it suggests the
precision with which average water levels (statistical quantities subject to
variation) can be estimated from spot elevations (measured quantities) taken
from static landforms. As explained above, this research relies on the gravel lags
that form at the bases of wave-cut bluffs to be geomorphic indicators of shoreline
events because they tend to form at or near the land-water interface and where
wave energies are relatively high. Elevations taken from the tops of these lags
serve as proxies for average water levels (Schaetzl et al., 2002). Because beach
sediments and shoreline features can move in response to water level

fluctuations, I must recognize that estimates of glacial Lake Algonquin water

45

levels based on geomorphic proxies are subject to uncertainty. Fortunately, the
range of contemporary Great Lakes water-level fluctuations (Table 2.3) provides
a convenient (albeit rough) estimate of this uncertainty. This research proceeds
by assuming the minimum vertical difference between two gravel lags that can
be used to discriminate two average glacial Lake Algonquin water levels is 3

meters.

Summary

Lake levels and shorelines are results of complex and dynamic
interactions among bodies of air, land and water, and gravitational forces. Such
interactions can occur over multiple spatial and temporal scales. Changes in lake
level, as well as rates of change in lake level, are generally recognized as
important controls on shoreline position, coastal processes, and coastal landform
changes. In general, shorelines migrate upward and landward as water levels
increase, and migrate downward and lakeward as water levels decrease.
Statistical techniques are usually required to summarize the distributions of
historic or contemporary lake-level fluctuations in terms of average lake levels.

Researchers interested in mapping and modeling paleolakes and
paleoshorelines must deal with difficulties associated with estimating statistical
lake levels by taking elevation measurements from relict shoreline features. The

precision of this method can be influenced by the choice of shoreline indicator as

46

well as the legacies of earth processes that have modified the landscape or
moved relict shoreline features since they were formed.

This research relies on the bouldery/ gravelly lags that formed at the bases
of relict wave-cut bluffs to be indicators of former shoreline positions (Schaetzl et
al., 2002). It is understood, however, given natural variability among local site
conditions, different lags that formed along the edge of the same lake surface
might have elevations that vary. The tradition of glacial Lake Algonquin
research and the later work of Morton and Speed (1998) and Moore (2000)
suggest the precision with which a lake level can be established by the elevation
of a wave-cut bluff alone is likely sub-meter, but knowledge about contemporary
water-level behavior indicates the precision may be, at the extreme, no better
than three meters. Accordingly, this research recognizes imprecision as a form
of uncertainty and proceeds by assuming the precision with which a former lake
level can be established by the elevation of a gravel lag situated at the base of a
wave—cut bluff is one meter, and the minimum vertical distance that can be used

to confidently discriminate different lake levels is three meters.

47

CHAPTER 3: METHODS AND FIELD CAMPAIGNS

Introduction

This chapter describes methods used to collect relict shoreline data and
build a glacial Lake Algonquin dataset. I begin by summarizing the work of
Schaetzl et al. (2002), which established a relevant methodology and produced an
initial dataset, which I inherited. I continue by recognizing opportunities to
improve upon the work they had done. Next, I review the prior mapping
campaigns led by Cowan (1985) and Karrow (1987) and describe how data they
collected were conflated with data collected during this work. I then report new
data I collected during a series of field campaigns designed to expand and
improve the geographic distribution of sampled shorelines. My report of relict
features at Cockburn Island, Ontario, for example, is a significant contribution to
the literature for no other report describes these features in detail. And, in light

of new data and recently published work, I offer reinterpretations of old data.

The initial glacial Lake Algonquin dataset

Uncertainty about the elevations, timing and extents of glacial Lake
Algonquin lake phases prompted Schaetzl et al. (2002) to conduct an extensive
survey of relict coastal landforms in northern Michigan. They targeted more
than 200 sites and were guided by descriptions of relict landforms in the
literature (e.g., Leverett and Taylor, 1915; Futyma, 1981; Farrand and Drexler,

1985; Schaetzl et al., 2002; and Krist and Schaetzl, 2001) and their interpretations

48

of features on 7 .5-minute USGS topographic maps. The authors investigated
sites to determine whether or not each one contains a relict wave-cut bluff
suitable for sampling. At suitable sites, Schaetzl et al. (2002) measured bluff
positions, rather than accept any previously published elevation values, because
the literature provides: a) few detailed descriptions about where previously
reported position measurements were actually made; b) few references to the
spatial reference systems employed (i.e., either the horizontal or vertical datum
was unspecified); and c) no assessments of data quality. Without such metadata,
the authors felt they could not assess confidently whether or not any previously
reported elevation value was valid, commensurate with other published data, or
acceptable for inclusion in further analysis. Their dataset contains 146 records
(Figure 3.1). Individually, each record represents the position of a relict shoreline
feature. In aggregate, their data reveal the spatial extents of four, possibly five,
glacial Lake Algonquin lake phases in northern Michigan (Schaetzl et al., 2002).
Schaetzl et al. (2002) concluded that pro- and postglacial lake levels can be
effectively identified, reconstructed, and correlated via examinations of elevation
data collected from wave-cut bluffs. They claimed their rebound curves and
isobase maps are more accurate than those published previously, but suggested
more geomorphologic and stratigraphic research is needed beyond their area of

study.

49

 

  
 
 
 
  
   
 
 

 

 

if I

l . > The Main Lake Algonquin shoreline was -- Current shorelines

i ,/ not generated for Canada's mainland. Show," of mm
<5; Lake Algonquin
>§ ONTARIO ' GPSpointnaardod
D- n Town
2
g :- Univ «Michigan
u Biologic Sutton
in Sugar Island
5’
-‘ ’ Neebish Island

 

 

 

. r:
Approximate ice.

margin position
State or province
bou -

 

 

    

 

PENNSYLVANIA

 

   

Figure 3.1: The study area explored by Schaetzl et al. (2002), points in the original
glacial Lake Algonquin dataset, and the extent of the Main phase of glacial Lake
Algonquin as they had determined it. Figure adapted from their Figure 1.

50

Opportunities to improve the glacial Lake Algonquin dataset

Several opportunities existed to substantially yet efficiently improve the
initial dataset built by Schaetzl et al. (2002); I capitalized on three. First, I
expanded the study area (see Figure 3.2) to include relict features at Sault Ste.
Marie (Cowan, 1985), St. Joseph Island (Leverett, 1913 and Karrow et al., 1987)
and Cockburn Island, Ontario (Leverett, 1913; Chapman and Putnam, 1966), as
well as others on Beaver Island, Michigan (Dietrich, 1978). Relict bluff features at
Sault Ste. Marie, Ontario and St. Joseph Island are important because they are
well-known and uniquely situated between Lakes Huron and Superior; they link
the evolutionary histories of these lakes. The correlations Cowan (1985) and
Karrow (1987) made between glacial Lake Algonquin phase names and stranded
shoreline elevations can be used to revise correlations made by Farrand and
Drexler (1985) and Schaetzl et a1. (2002) in northern Michigan. Second, the initial
geographic distribution of sampled positions (Figure 3.1) is not oriented along
the generally accepted direction of differential isostatic uplift (approx. N 15°E;
after Futyma, 1981), but obliquely to it (approx. N 35°W). The consequences that
such an orientation has on the process of estimating rebound trend parameters
are not known, but it seems reasonable to treat any such parameters as
provisional until additional data can be collected along, rather than normal to,
the uplift trend. Collecting and integrating data from the islands mentioned
above adds important features to the glacial Lake Algonquin dataset and much

needed support to unsampled sectors along the former water planes.

51

 

 

  

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i- ..‘_.....4...‘._,....._...

 

Figure 3.2: Map of the current study area with names of places and features
mentioned in the text. County boundaries and names added for reference.

52

Last, Schaetzl et al. (2002) and Drzyzga et al. (2002) used an undersized set
of ground control points (n=8) to assess the quality of sampled shoreline
elevations (n=146). Drzyzga et a1. (2002) made simplistic assumptions about the
distribution of error in the dataset, which may or may not represent the actual
distribution of error. So, I collected a larger set of ground control points (n=24).
The larger set of ground control points is useful for better assessing the quality of
the glacial Lake Algonquin data set and mitigating the effects of an apparent
error process (e.g., a systematic bias or spatial pattern). The accuracy assessment

is reported in Chapter 4.

Shoreline identification, bluff selection, and sampling methods

Frank Taylor (1895) stressed the value and importance of studying the
ancient islands of glacial Lake Algonquin. Notable examples include the ancient
Munuscong Islands in Mackinac County, Michigan (Taylor, 1895) and proto-St.
Joseph Island (Karrow, 1987), proto-Cockburn Island (Chapman and Putnam,
1966), and proto-Beaver Island (Dietrich, 1977). Accordingly, I focused my
attention and fieldwork on contemporary landforms that may have existed as
islands in glacial Lake Algonquin and tried to collect data from as broad an area
as possible.

I inherited the dataset and employed the same set of shoreline

identification and bluff selection methods used by Schaetzl et al. (2002: 405-406).

And, like they did, I relied on the bouldery/ gravelly lags that form at the bases

53

of wave-cut bluffs to be geomorphic indicators of ancient shorelines (Figure 3.3).
Using the same indicator ensures similar reliability and consistency
characteristics between data collected during their campaign and new data
collected during mine. Similarities notwithstanding, I provide a summary of
methods below because several differences do exist between the GPS leveling
technique and data processing methods I used and those that Schaetzl et al.
(2002) used. For example, I take advantage of the latest geoid model (GEOID03,
Roman et al., 2004) that is a better approximation of mean sea level throughout
the United States than the GEOID96 geoid model (Smith and Milbert, 1999) they

used.

 

wave—cut bluff f/

debris (colluvium & slopewash)

  
 
  

GPS

former mean water level

. “fig-”WM b h
wave-bunt terry , _ // enc
./’/

/ (”11-7"

_ .6532’”~

bouldery lag

 

 

 

Figure 3.3: Schaetzl et al. (2002) used bouldery/ gravelly lags at the bases of
wave-cut bluffs as shoreline indicators. Figure was adapted from their Figure 2b
(p.405).

54

First, I collected 7.5-minute USGS topographic map sheets for all locations
within the study area. I also collected 1:50,000 Canadian Topographic Map
sheets to supplement coverage of Cockburn Island, St. Joseph Island, and Sault
Ste. Marie, Ontario. Field notes taken during previous campaigns as well as
extant literature (e.g., Leverett and Taylor, 1915; Hough, 1958; Dietrich, 1978; and
Karrow, 1987) were used as guides for targeting likely sites with relict wave-cut
bluffs. Initial selections were limited to only those features that are landward of,
and higher than, the generally accepted N ipissing water surface (Goldthwait,
1910). I plotted extant data and new potential bluff targets on topographic map
sheets to identify areas with little data.

Next, I visited targeted sites. A target was selected for sampling if it
exhibited a conspicuous bluff-to-beach morphology and presented a well-
defined bluff toe. If a target exhibited a conspicuous bluff-to-beach morphology
but not a well-defined toe, then I traveled along the feature (for up to several
hundred meters in either direction of the initial site) in search of a ”best” site that
contained a well-defined toe and a relative paucity of forest cover (to facilitate
radio signal reception from orbiting GPS satellites). Locations that evinced
anthropogenic change or bluff failure are not suitable locations for sampling and,
so, were not sampled.

Third, an initial position was selected along the bluff toe. Soil was
excavated with a bucket auger to a maximum depth of 1.5 meters. If a

bouldery/ gravelly lag (Figure 3.3) could not be detected, then sampling

55

proceeded down slope at successively lower locations until a buried lag was
found. (Fortunately, at many sites a conspicuous boulder lag is present below
the bluff.) Field notes were taken at the ultimate location to describe the site and
record depth to the buried gravel lag. Elevation measurements, which were
taken at the land surface, were adjusted downward to account for the vertical
distance between the land surface and the buried lag. Also, when weather
permitted, an image of the site was recorded with a digital camera.

And fourth, real-time differential Global Positioning System (GPS)
technology was employed to measure relict shoreline positions. When used
correctly, GPS leveling offers at least five distinct advantages over other field
methods: a) on average, position measurements {x,y,z triplets} can be made
quickly and with sub-meter errors; b) position values collected among scattered
field sites can be georeferenced to the same spatial reference system; c) field
equipment is light-weight and portable; d) fieldwork can be conducted
effectively and efficiently by one person, which precludes the need for a second
person to work the other end of a level line; and e) all position data are recorded
and stored in digital form, which facilitates translation into data formats that can
be analyzed within a (313 or spreadsheet environments.

I planned and organized data collection activities in three important ways
to take best advantage of GPS technology. First, the field season was limited to
leaf-off conditions (i.e., late fall) because summer-time leaf canopies can

obfuscate, perturb, or block GPS radio signals. The winter leaf-off season was

56

also avoided, however, because regional winter snow blankets ground features
and inhibits exploration. In the field, the GPS receiver was mounted onto a
tripod and raised two meters above the ground. Second, all data were collected
during temporal windows that framed optimal GPS satellite constellation
configurations (i.e., VDOP S 3.0) 1. GPS receiver software can manipulate and
tumble numbers under a plethora of constellation configurations, but relatively
few configurations offer geometries sufficient for taking accurate and precise
vertical measurements. Trimble’s Quick Plan software (Trimble Navigation
Limited, 2002) and current satellite ephemeris data were used to identify and
select suitable VDOP windows. Data collection activities were scheduled and
limited to these windows only. And third, a point-averaging technique was used

to estimate position at each site. The point-averaging technique requires

 

1 A Dilution of Precision (DOP) value is an estimate of the quality of a GPS
position. For a given point in time, the DOP value takes into account the location of
each GPS satellite relative to the locations of others in the constellation, and their
geometry in relation to the GPS receiver (Reilly, 2002). A low DOP value suggests a
relatively high probability of taking an accurate measurement. A low VDOP (Vertical
Dilution of Precision) suggests a relatively high probability of taking an accurate vertical
measurement. Because this research is concerned with taking accurate vertical
measurements, primary emphasis is placed on obtaining low VDOP values during data
collection activities. Most satellite-viewer geometries that are optimal for taking

accurate vertical measurements also allow taking accurate horizontal measurements.

57

multiple measurements of the same feature to be made. Collecting a sample of
measurements and summarizing it in terms of average coordinate values and
precisions, rather than collecting a single measurement, reduces the risk of
accepting data with large random errors. Schaetzl et al. (2002) used the point
averaging technique and collected a sample of no less than 100 position
measurements at each bluff site. They achieved reliable results with the
technique, but had to discard some valuable data because, for some sites, many
of the 100+ measurements were deleted during data processing (pers. comm.)
Collecting a larger sample at each site would have helped preserve their data.
So, for this work, I collected a larger sample of no less than 300 position
measurements at each bluff site. All horizontal locations are referenced to the
North American Datum of 1983 (N AD83). All elevations were referenced first to
the World Geodetic System 1984 (WGS84/ C3873) ellipsoid model and later

converted to orthometric heights (see below).

Data processing

Data files (one sample of shoreline measurements per file) were processed
using Trimble Pathfinder Oflice (GPS) and Microsoft Excel (spreadsheet) software.
Data processing followed this model:

First, each file was assigned to one of two groups: those with position data
that were differentially corrected in the field, and those that were not. The radio

link between a GPS receiver and the satellite that delivers OMNIStar’s real-time

58

correction service is sometimes lost behind local obstructions (e. g., a massive
bluff or a dense forest condition). Each file with uncorrected data required post-
processing using differential-correction data made available via the network of
National Geodetic Survey, Continuously Operating Reference Stations (CORS).

Next, the spatial distribution of individual position measurements
collected at each bluff was examined using a scatterplot matrix. The 3-D
distribution was examined and filtered of positions associated with conspicuous
multi-path errors (i.e., a linear pattern of sequential measurements that drifted
over distances greater than one meter and suggested the incoming radio signal
was bouncing off a nearby object) or indicators of poor satellite geometries (i.e.,
VDOP values > 3.0). The remaining set of acceptable positions was summarized
geometrically to support average x, y and z coordinate values and measures of
precision (i.e., standard deviation).

Elevation values were processed one step further to convert heights
referenced to the WGS84 ellipsoid to orthometric heights, which are referenced
to the North American Vertical Datum of 1988 (N AVD88) and tied to the familiar

notion of mean sea-level. Orthometric height (H) is calculated as:

H=h~N [Eq. 1]

where: h is the average of sampled heights above the WGS84 ellipsoid as

obtained from GPS leveling; and N is the geoidal undulation at that location and

59

obtained from the GEOID03 model (Roman et al., 2004). In Michigan, users of
GEOID03 are able to convert GPS-measured ellipsoid heights to orthometric
heights to within 2.7 cm of traditional land-based geodetic measurements
(Roman etal., 2004: 11, Table 1).

Last, field notes, digital images, and feature positions were reviewed a
final time. Each elevation value was adjusted downward to account for the
tripod height (two meters) any distance between the land surface and the buried
gravel lag. Feature positions associated with conspicuous wave—cut bluffs were
added as records to the glacial Lake Algonquin dataset and exported to an ASCII
text file, which is readable by common GIS or spreadsheet applications. Feature
positions not associated with conspicuous wave-cut bluffs are retained in a
supplemental database.

This research employs the same sets of selection criteria, GPS equipment
(T rimble XRS receiver, antenna and software) and real-time differential
correction procedures used by Schaetzl et al. (2002). So, by following the same
data collection methods and using the same field equipment, it is reasonable to
assume that the data collected during this exercise can be conflated with data
collected during the previous work. Yet, to ensure data are conflated properly in
every manner, I utilized the original and unprocessed set of GPS data files
collected by Schaetzl et al. (2002), which I inherited, and processed each
according to the model describe above. The only notable difference in methods

was that Schaetzl et al. (2002) employed the GEOID96 geoid model (Milbert and

60

Smith, 1996) and this work uses the current GEOID03 geoid model (Roman et al.,
2004) to convert heights measured above the ellipsoid to elevations tied to the

N AVD88. The current geoid model is considered the most accurate available.

Summary of prior mapping campaigns

Sly and Lewis (1972), Cowan (1985), and Karrow (1987) collected
paleoshoreline data at Manitoulin Island, Sault Ste. Marie and St. Joseph Island,
Ontario, respectively, and correlated their features with Algonquin lake phases
named by Deane (1950: Ardtrea, Upper Orillia and Lower Orillia), Stanley (1936:
Wyebridge, Penetang, Cedar Point and Payette) and Hough (1958: Sheguiandah
and Korah). Their campaigns relied on the bases of wave-cut bluffs to be
indicators of former lake levels and they employed survey-grade equipment to
measure paleoshoreline elevations precisely and accurately. Moreover, features
at Sault Ste. Marie and St. Joseph Island are situated near others surveyed in
Northern Michigan, so I used them to inform my classification of relict features
in Northern Michigan and, in effect, revise some previous classifications
proposed by Farrand and Drexler (1985) and Schaetzl et al. (2002).

Cowan (1985) mapped Quaternary sediments at Sault Ste. Marie, Ontario,
and concluded the sandy terrain situated between the exposed Canadian Shield
(to the north) and St. Marys River (to the south) exhibits a descending sequence
of stranded shoreline features. I-Ie associated the uppermost (at 309 m) with the

Main phase of glacial Lake Algonquin. Although Cowan reported elevations, he

61

did not report the locations of features he surveyed, so readers of his report
cannot use it as a field guide. I contacted Dr. Cowan to inquire about the
locations of bluff features he surveyed and, graciously, he sent me copies of his
field notes and data. He also sent copies of topographic maps, on which he
marked the locations of benchmarks, level lines and relict bluffs. Given this
wealth of information, I was able to combine his surveyed elevation data (2) with
corresponding location data (x,y) that I interpolated from each topographic map.
According to Cowan (1985), his elevation data are accurate to within 30
centimeters. The location data I interpolated from topographic maps are
accurate to within 25 meters. Table 3.1 summarizes Cowan’s (1985) results

(Table 1, p34).

Table 3.1: Approximate elevations for glacial Lake Algonquin water planes and
the Nipissing water plane at Sault Ste. Marie and Manitoulin Island, Ontario
(Cowan, 1985).

 

 

Elevation at Elevation at
Sault Ste. Marie (m) Manitoulin Island (m) Lake phase
309 309 Main
302? - Ardtrea
295 287-296 Upper Orillia
? - Lower Orillia
275? 271-276 Wyebridge
265 267 Penetang
257 259 Cedar Point
247 244 Payette
233i: 233 Sheguiandah
210 212 Korah
198 198 N ipissing

 

62

Karrow (1987) mapped Quaternary sediments at St. Joseph Island, Ontario
and surveyed stranded shoreline features. Specifically, he measured the
elevations of wave-cut bluffs and the tops of beach bars. He projected his
surveyed elevation data onto a line of profile oriented along the presumed
direction of maximum uplift (N15°E; after Futyma, 1981). Karrow compared his
projected elevation data to the set of previously named water planes (Hough,
1958; Sly and Lewis, 1972; and Cowan, 1985) and concluded, despite some
inconsistencies, that all but the central hill of St. Joseph Island was submerged by
the Main phase of glacial Lake Algonquin. I summarize Karrow’s Figure 5
(p116-117) as Table 3.2 to facilitate comparison with data I collected in this work.
Table 3.2: Lake level elevations for glacial Lake Algonquin water planes and the

N ipissing water plane at the southern end of proto-St. Joseph Island, Ontario
(Karrow, 1987).

Elevation (m) Association

 

280 Main Algonquin

27 2? Ardtrea

266? Upper Orillia

258? Lower Orillia

240? Wyebridge

232 Penetang

225 Cedar Point

212 Payette

200 Sheguiandah
- Korah

196 Nipissing

 

Readers of Karrow’s (1987) report cannot use it as a field guide, so I

contacted him to inquire about the locations of the bluff features he surveyed.

63

He graciously sent me copies of his survey data and marked topographic maps
with the locations of relict wave-cut bluffs he surveyed. Given this information, I
was able to combine his surveyed elevations (z) with corresponding location data
(x,y) that I interpolated from topographic maps (Figure . In related work,
Karrow (1988) indicates his surveying method yield elevations with decimeter-
level accuracy. The location data I interpolated from topographic maps are
accurate to Within 25 meters, which is the precision afforded by the width of a

printed contour line at the 150,000 scale.

Mapping campaigns conducted for this work

Frank Taylor stressed the importance of ancient islands when he wrote:

”. . . [they] can hardly be overestimated, especially if they are
situated well out from the mainland. Each one furnishes a new
point of support for the restoration of the water plane and must
prove valuable in the ultimate study of the earth’s history as
disclosed in the deformation of former water levels" (Taylor, 1895:

28)

Accordingly, I focused much of my attention and fieldwork on contemporary
landforms that may have existed as islands in glacial Lake Algonquin. I visited
sites with potential bluff features between June 2000 and December 2003. The
subsections that follow document features and observations I made during these

visits. In the text I provide maps and refer to field sites using a system of unique

64

site identification numbers (e. g., SID642) and report features elevations in meters.
Figure 3.4 can be used to reference each of the smaller—scaled area maps. Last but
not least, I report correlations I made between elevations taken from relict wave-

cut bluffs and named glacial Lake Algonquin lake phases.

65

 

 

 

     
        
 
 

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WEXFORD l MISSAUKEE ‘ ROSCOMMON f OGEMAW .1 Figureenfifgg

 

 

Figure 3.4: Index map for smaller-scaled maps that show field campaigns and
field sites mentioned in this chapter.

Cockburn Island, Ontario

Leverett (1913) and Chapman and Putnam (1966) mentioned that a
possible islet of glacial Lake Algonquin exists at Cockburn Island, Ontario, but
neither they nor subsequent writers have offered a detailed description of the
supposed islet or data to support their observations. P. F. Karrow (personal
communication, 2003) surveyed a line in 1991 across the northern part of
Cockburn Island to the supposed islet, but his data remain unpublished as part
of a larger study of nearby Manitoulin Island.

I conducted fieldwork on Cockburn Island during October, 2003.
Transportation to and from the Island, lodging, and access to an off-road vehicle
were provided by Huron Timber Company of Thessalon, Ontario, which owns
more than 80 percent of the ~100 km2 island. Cockburn Island has no permanent
residents, paved roads, or services of any kind; the sole town of Tolsmaville
evinces former life as a port community but is now defunct. Concession roads
and logging trails offer limited access to interior portions of the island, but
accessing most relict features must be achieved on foot. I encountered Mr.
Harold McQuarrie, a seasonal island resident, by chance. He maintains a hand-
drafted map of island features that depicts logging trails, property ownership
boundaries, concession- and patent-holder names, and basic hydrographic
features. Mr. McQuarrie's map (McQuarrie, 2000) greatly facilitated my efforts to
traverse the Island and approach bluff targets. Figure 3.5 shows Cockburn Island

and identifies field sites visited and discussed in the text.

67

 

5153:27. . ‘ "
152: 25.27%?”
316: 278.4m
' .<.-'137'272.9m ~ -
" 36274.1":

 

Figure 3.5: Relict bluff sites at Cockburn Island, Ontario. Sites are labeled with a
unique site identification number and an elevation value (e.g., 642: 200 m).

I focused attention on a small upland called McCaigs Hill. McCaigs Hill is the
highest feature on Cockburn Island, approximately 2 km2 in size, composed of
unconsolidated sediments, and divided roughly into quadrants by two
intersecting concession roads. McCaigs Hill exhibits a relatively smooth surface
that dips visibly southward; only a shallow saddle, which trends NNE-SSW, and
scattered well-rounded boulders interrupt the surface. Soil samples taken along

the surface (to a maximum depth of 1.5 meters) revealed red-brown sands and

68

few stones; clay content tended to increase with depth. Much of the upland
surface and some of the eastern and southern slopes were once cleared of forest
cover and are now covered by grasses; relict landforms in these areas are
exposed plainly and clearly. A small area in the northeastern section of McCaigs
Hill is known locally as Scotch Block, for a settlement of Scottish families that
once inhabited the site.

The steep sides of McCaigs Hill exhibit strong bluffs at four distinct
elevations (280, 272, 266, and 259 m); two can be traced around the Hill, but all
are interrupted in places by localized bluff failures or road cuts. The two highest
(~280 m: SID128, 136, 141, 144, 152 and 154; and ~272 m: SID127, 137, 138, 142,
153 and 155) are conspicuous and well-defined (Figures 3.6 and 3.7), particularly
in the eastern side of the Hill. Two lower sets of bluffs (at ~259 m: SID126 and
157; and at ~266 m: SID145 and 156) are also conspicuous and well-defined, but
on the northwestern side of the Hill only. The bluff at 259 m (height >16 m) is
well preserved, but shrouded by dense tree cover along most of its length. All
other bluffs are absent where this bluff is strongest; it visibly truncates the next
higher bluff (266 m) and, perhaps, an intermediate bench. The bluff changes
character rapidly, for it shortens into a low bluff and then degrades into three
wave-cut scarps or bars that run in a south-southeasterly direction away from
northwestern side of the upland. The bars are composed of rounded gravels and
are relatively tall, narrow and compactly spaced at locations near the bluff site,

but tend to shorten, widen and separate as they curve away from the Hill.

69

 

Figure 3.6: Image of a relict bluff on the south side of McCaigs Hill, Cockburn
Island, Ontario.

lake bottom

 

Figure 3.7: Diagram of the relict bluff shown in Figure 3.6. Shoreline positions
were measured at gravel lag situated at the base of the bluff.

7O

 

A pair of lower shorelines is also present (at ~230 m: SID132, 146, 149 and
150; and at ~222 m: SID131, 133, 147, 148, 151 and 158). They are situated several
kilometers from McCaigs Hill and outline what must have been younger and
larger proto—Cockburn Islands. I characterize these two shorelines as a pair
because each occurs in close proximity to the other. For example, at some
locations these features present as a set of gravelly bars, with one situated several
meters higher than the other. At other locations they appear as a combination of
erosional bluff and bar or as a set of erosional bluffs. Incidentally, this pair is the
highest set of relict shoreline features connected to bedrock outcrops. I found
small dolomite outcrops at the northern and southern tips of this ancient island
which might have supplied the parent material for the gravelly bars.

Cedar swamps sandwich narrow hardwood stands situated along the
sloping sands and gravels between the bluffs at the 222 m and 230 m elevations
and might hold organic material suitable for radiocarbon analysis and dating.
Lumbermen were harvesting hardwoods in this area and during the time of
fieldwork. Their safety concerns prohibited me from accessing features at these
worksites, so I consider the survey of relict features as incomplete.

Relict bluffs at Cockburn Island have elevations that correspond with the
elevations of relict bluffs stranded at Sault Ste. Marie, St. Joseph Island, and
Manitoulin Island as well as others in the eastern half of Michigan’s Upper
Peninsula. Table 3.3 lists the elevations of relict bluffs at Cockburn Island and

the names of coplanar water levels at nearby St. Joseph Island.

71

Table 3.3: Approximate elevations of glacial Lake Algonquin water planes
measured at Cockburn Island, Ontario.

Approximate elevation (mL Water plane / lake phase

 

280 Main

272 Ardtrea

266 Upper Orillia
259 Lower Orillia
230 Penetang

222 Cedar Point

 

Cowan (1985) describes relict shoreline features at Sault Ste. Marie,
Ontario and argues they are directly comparable with others at Little Current,
Ontario (Sly and Lewis, 1972), because respective interpretations of both "Main
Algonquin and Nipissing levels are within one meter of each other" (p.36). If
Cowan's argument is correct, then both locations have experienced similar rates
of, and cumulative amounts of, isostatic recovery over time. Cartographically,
an isoline of paleolake-plane elevation can be drawn to represent the apparent
connection between these two locations (Figure 3.8, 309 m). Such a line is
oriented similarly to other isolines drawn by Goldthwait (1910:38), Leverett and
Taylor (1915:429), Hough (1958256) and Clark and Persoage (1970).

Cockburn Island is situated south of the isoline drawn between Sault Ste.
Marie and Little Current, Ontario (Figure 3.8). Given the generally accepted
trend of increasing isostatic rebound across the region (N15°E; Futyma, 1981)
and given the relative location of Cockburn Island with respect to this isoline, it

is reasonable to expect that intersections between glacial Lake Algonquin water

72

planes and the Cockburn Island land surface occur today at elevations lower
than those measured at Sault Ste. Marie and Little Current, ON (309 m, after
Cowan, 1985: p. 34). The highest shoreline measured at Cockburn Island is at
280.2 m, which is lower than the highest shorelines found at Sault Ste. Marie and
Little Current, and proximate to the highest shorelines found at St. Joseph Island,
ON (280 - 285 m, after Karrow, 1987) and in northern Michigan (282 - 285 m,
after Schaetzl et al., 2002). The highest shorelines at St. Joseph Island and in
northern Michigan are associated with the Main phase of glacial Lake
Algonquin, so it seems reasonable to infer from the near-equivalent elevation of
the highest shoreline at Cockburn Island that McCaigs Hill, a small upland, was

an ancient islet of the Main phase of glacial Lake Algonquin.

 

2 I Y
1 1" am 32w

r i l
U) ,_ . . Al
Sault '1 T i '
Lake " , ' ' '
Supenim‘ ( K/ " \
fl

   
 
 
  

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. » 'x_ if 1
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l

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W, \N Qflsland Cockburn mi. 1. w}! i
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Michigan ,3 “\\“‘3 ISIand . _L".-., /,.-j /
w—w} \lw' L04. Manitoulin liuck j}?
V./\.\ (3 filll‘o’] Island \ K ’

2 saw 32w ‘~/
1

Figure 3.8: Apparent contours across the Main Lake Algonquin water plane.

 

 

73

 

Interpretation of lower shorelines is problematic, however, because they
cannot be correlated consistently with water planes named at nearby places. For
example, Schaetzl et a1. (2002) argued that only the Main, Ardtrea, Wyebridge
and Payette phases can be interpreted consistently among the data they collected
in Michigan. This set of four lake phases is not sufficient for interpreting the six
water planes I observed at Cockburn Island. Based on their isoline maps of bluff
elevations (Schaetzl et al., 20022411) bluffs at Cockburn Island that occur at 280,
272, and 266 m correlate closely with their Main, Ardtrea and Wyebridge phases,
respectively, the bluffs stranded at 259, 230, and 222 m have no correlates.
Karrow (1987 :118) reports many relict shoreline features on St. Joseph Island that
appear to correspond to Upper Group and Lower Group beaches, but he claims
his data are insufficient ”to clearly distinguish particularly consistent and well-
developed water planes" below the highest one. Yet, assuming St. Joseph Island
is to Cockburn Island as Sault Ste. Marie is to Manitoulin Island, I use Karrow’s
lake plane profiles (Figure 5, p116-117) to extrapolate named water levels from
St. Joseph Island to Cockburn Island. In descending order, paleoshorelines at
Cockburn Island correspond with the Main, Ardtrea, Upper Orillia, Lower

Orillia, Penetang and Cedar Point water planes.

Sugar Island, Michigan
Schaetzl et a1. (2002) surveyed two relict features at Sugar Island, which is

situated in the St. Marys River and between Sault Ste. Marie and St. Joseph

74

Island, Ontario (Figure 3.9). The authors measured a high feature twice (240 m:
SID395 and 407) and correlated it with the Payette phase. They measured a low
feature twice (228 m: SID396 and 453) but correlated one measurement with Lake
Minong phase of Lake Superior and attributed the other to an unnamed ”lower”
phase of Lake Huron. In light of data available in nearby Canada, I believe the

lower feature is best correlated with the Sheguiandah phase.

 

L: 1’0 r3 v

‘1

 

 

Figure 3.9: Relict bluff sites at Sugar Island, Michigan. Sites are labeled with a
unique site identification number and an elevation value (e.g., 642: 200 m). Also
shown are the locations of features surveyed by Cowan (1985).

75

 

Rexford, Michigan

Main Algonquin occupied a ”sizeable part of Whitefish Bay in eastern
Lake Superior” (Cowan, 1985: 34). Farrand and Drexler (1985) recognized
several post-Algonquin lakes, ”at least through Sheguiandah” (p30), that
transgressed into the Superior basin; they correlated features found near Pendills
Bay with the Wyebridge and Payette phases. A careful read suggests, however,
that Farrand and Drexler (1985) were not fully confident in their assignments of
Algonquin phase names to the features they studied (i.e., ”Wyebridge(?)”, p29).
In other work, Futyma (1981) identified Main and Battlefield (now deprecated)
type features in this same region, but did not correlate features having
intermediate elevations with named lake phases.

Schaetzl et a1. (2002) surveyed 16 features in western Chippewa County,
MI (Figure 3.10) and based their correlations on those named previously by
Farrand and Drexler (1985). The highest stranded bluff in this region, located 3
km due east of McNearney Lake, has a toe elevation of 281.9 m (SID393) and is
correlated with Main Lake Algonquin; no higher bluff exists in this region. Two
nearby features were measured at 262.1 m (SID392) and 259.5 m (SID404) and the
authors assigned them to the lower Wyebridge phase. Surprisingly, Schaetzl et
a1. (2002) associated features near Dollar Settlement and stranded at ~232 m with
Lake Minong. Farrand and Drexler clearly describe a bench near Dollar
Settlement ”at 213 to 219 m" to be ”a good candidate for the Minong shoreline”

because it occurs in the Pendills Lake embayment immediately west of Nadoway

76

Point and does not occur ”to the east on the Lake Huron slope” (Farrand and

Drexler, 1985: 29). Confusion about these features prompted me to reinterpret

  
  

     
 

 

 

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Figure 3.10: Relict bluff sites near Rexford, Michigan. Sites are labeled with a
unique site identification number and an elevation value (e. g., 642: 200 m).

The highest stranded shoreline in this region has an elevation of 281.9 m.
Nearby features associated with the Nipissing water plane rest at 198 m. The

elevations of Main Algonquin and Nipissing features correspond very closely

with those measured at St. Joseph Island and do not correspond with those
located, for example, north of Sault Ste. Marie (see Figure 3.2). Assuming St.
Joseph Island is to the Pendills Bay area as Manitoulin Island is to Sault Ste.
Marie (after Cowan, 1985), I used Karrow’s lake plane profiles (Figure 5, p116-
117) to correlate features at Pendills Bay with those at St. Joseph Island. In my
opinion, correlating two sequences of nearby features with near equivalent
elevations makes better sense than extrapolating lake levels from either Sault Ste.
Marie or the Penetang Peninsula as Farrand and Drexler (1985) seem to have
done. I report updated associations in Table 3.4. In effect, I have recognized
connections among relict features stranded in the Pendills Bay area and others
stranded at St. Joseph Island and Cockburn Island (Figure 3.5). Having surveyed
features in the Pendills Bay area, as well as those at Cockburn Island, I believe

the relative strengths of bluffs along each sequence are better matched.

Table 3.4: Approximate elevations of glacial Lake Algonquin water planes and
the N ipissing water plane measured in western Chippewa County.

Approximate elevation (m) Water plane / lake phase

 

 

280 Main
273 Ardtrea

- Upper Orillia
259 Lower Orillia
240 Wyebridge
232 Penetang
198 N ipissing

 

78

The Munuscong Islands

Taylor (1895) reported observations and provisional height measurements
taken along a set of Algonquin strands situated ~1.5 km north of Hessel, MI.
According to Taylor, the Munuscong Islands were the only landforms that
interrupted the highest Algonquin water surface ”between Mackinac and the
Canadian Highlands back of Sault Ste. Marie" (p28). Although the author
reports that at least three islands remain, he visited only two: the one closest to
Hessel and ”irregular in outline” (p.26); and a smaller island situated northeast
of Hessel that exhibited ”precipitous cliffs of limestone 75 to 100 feet in height”
(p26). Taylor did not visit the largest of the three islands he mentioned, which is
situated northwest of Hessel.

Eighty-five years later, Futyma (1980) revisited the Munuscong Islands.
Unfortunately, his report offers no new information about these landforms. A
careful review of Appendix A (Futyma, 1980) indicates the author focused on just
the one island closest to Hessel and relied only on Taylor's (1895) and Leverett
and Taylor’s (1915) early findings.

Twenty years after Futyma, Schaetzl et al. (2002) targeted these islands,
were finally able to access and study a portion of the unvisited northwestern
island, and provided new information. In all, Schaetzl et al. (2002) measured 10
positions in the Munuscong Island region. They identified shorelines associated

with the Main, Ardtrea and Wyebridge phases along the central island closest to

79

Hessel; the Wyebridge and Payette phases along a minor islet; and the
Wyebridge, Payette and lower phases along the large northwestern island.

I conducted fieldwork in the Munuscong Islands region, visited old sites,
and collected five new position measurements (Figure 3.11). I focused most of
my attention on the large northwestern island. The upland covers the better part
of 9 km2 and was accessible to me only via a poorly maintained two-track named
Fish Road. All other points of entry, particularly the one along Criderman Road,
are gated and posted. In the southern half of Sec. 14 T43N R2W, I observed two
bluffs, one massive (height > 35 m) and one lesser, but only by comparison.
Huge limestone boulders litter the bases of these giant bluffs. The sheer sizes of
these well-rounded boulders, perched atop beach sand, clearly imply powerful
water action. Unable to receive GPS radio signals at positions along the bluff toe,
I traced the features northward into the northern half of Section 14. There I was
able to measure positions along the upper and lower shorelines. The upper
shoreline is stranded at 266.9 m (SID172) and I associate it with the Main phase.
The lower shoreline is stranded at the 259.7 m (SID171) plane and, I believe, is
associated with the Ardtrea phase. I measured a third shoreline position in Sec.
26 T43N R2W at the 264.3 m plane (SID169), which I believe is also associated
with the Main phase. I attempted to maneuver toward the northwestern side of
the large island, but nearly every pathway and trail is gated or posted. I believe
the northwestern side holds additional massive bluffs, which are visually

apparent from nearby Interstate 75, and I hope to study them someday.

80

 

 

 

 

 

(is); ‘
' 9 ,. 166:223.8m
3592221 ~2m‘.167:224.5m
9166:222.3m
Chippewa County
3.2323355"
I . m
319.241.4111 . . The
172:266-9m_i'171:259.7m Munuscong
Islands
_ . o449:227.0m
169:262.0m+ 1741250-0'“ _
. 448:249.5m
“(J-2650'” 450:258.4m
» . ,_ 451:265.7m°. . ,2 . ‘1
' Mackinac County i
“2241.4“..- 3' 3.: 17:256-2m I l
3042442111 l ,
o 4 6 8Knometer§ J
i
I . .

3 4 5Miles Hessel

Figure 3.11: Relict bluff sites in the Munuscong Islands region. Sites are labeled
with a unique site identification number and an elevation value (e. g., 642: 200 111).

An apparent fourth and easternmost island of the Munuscong Island
chain remains unstudied. Much of the land area is currently held by mining
interests; a large quarry occupies large portions of Sections 3 and 10 of T42N R1E
and, perhaps, is the site where Taylor (1895226) observed his ”precipitous cliffs of
limestone.” Table 3.5 lists the glacial Lake Algonquin water planes I associated

with paleoshoreline elevations in this region.

81

Table 3.5: Approximate elevations of glacial Lake Algonquin water planes
measured in the Munuscong Islands region.

Approximate elevation (m) Water plane / lake phase

 

265 Main Algonquin
258 Ardtrea

250 Upper Orillia
242 Lower Orillia
220 Penetang

 

Kincheloe, Michigan

The Kinross State Correctional Facility (formerly the Kincheloe Air Force
Base) is situated atop a raised terrace; a conspicuous wave-cut bluff marks nearly
every side. Schaetzl et a1. (2002) surveyed the toe of a substantial bluff on its
eastern flank and correlated its 221 m elevation with Lake Minong (SID389). I
surveyed the same feature at three locations along 2 km of its length (SID166, 167
and 168) and obtained an average elevation of 223 m (Figure 3.11). Farrand and
Drexler (1985), working northwest of Kincheloe, MI in the Pendills Bay area,
identified Lake Minong shorelines at elevations between 213 and 219 m and
contend a ”Nadoway Point-Gross Cap sill” (p29) retained Minong waters in the
Superior Basin until it was downcut (or breached by inflow from Lake Agassiz),
thereby lowering water level even further. In light of Kincheloe’s relative
location with respect to the proposed Nadoway Point-Gross Cap sill and
situation with respect to St. Joseph Island (~30 km), I believe the stranded bluff at

Kincheloe is too high to be associated with the Minong phase of Lake Superior. I

82

believe this feature is better correlated with the Cedar Point water level of glacial

Lake Algonquin.

Mackinac Island, Michigan

Leverett and Taylor (1915) identified an ancient island at Mackinac Island,
MI, which is uniquely situated near the confluence of Lakes Michigan and
Huron, and between the Munuscong Islands in Michigan’s Upper Peninsula and
the Pellston/ Riggsville Islands region of the Lower Peninsula. They describe
”splendid displays” of ”all the beaches from the upper Algonquin down”
(Leverett and Taylor, 1915: p424) and assigned the now deprecated Upper
Group, Battlefield and Fort Brady labels, in descending order, to three groups of
successively lower relict features.

Stanley (1936) studied relict shoreline features along the Penetanguishene
Peninsula (a.k.a. Penetang Peninsula) of Ontario and compared water levels
there with those he and Leverett and Taylor (1915) observed at Mackinac Island.

I include an excerpt from his report here (Stanley, 1936:1955):

On theoretical grounds, all the Algonquin planes here discussed
should be separated by similar intervals wherever the total amount
of Algonquin deformation is equal, provided that tilting between
Algonquin and Nipissing times proceeded always in the same
direction. For instance, on Mackinac Island there should be a

shoreline about 90 feet lower than the highest Algonquin (809-812)

83

in order to correlate with the Wyebridge shoreline in the Penetang
area (which is 90 feet below the Algonquin in that region). The

type Battlefield beach (719) on Mackinac Island fulfills this

requirement exactly.

Stanley’s provisional correlation of Ontario’s Wyebridge type beach and
Mackinac Island’s Battlefield beaches required a leap of faith considering that he
could not identify the Wyebridge shoreline near Wasaga Beach (see Stanley,
1936: 1938 and Table 3 on page 1951) and his work at Mackinac Island yielded, in
his own words, ”poor results” (p1955). He expressed uncertainty regarding ”just
how the lower Algonquin beaches of the Mackinac region fit in with those near
Penetang” (p1955). Deane (1950: 74), working later and near Lake Simcoe,
Ontario, argued Wyebridge features are ”not strong” and indicate ”only a short
pause of Lake Algonquin at this level.” He also reported elevations and relative
strengths of features formed along four upper lake levels (Main, Ardtrea, Upper
Orillia and Lower Orillia) and characterized the Main and Upper Orillia
paleoshorelines as strongest.

Uncertainty about the elevations of features at Mackinac Island and their
correlations with others prompted Schaetzl et al. (2002) to visit the island and
survey relict features there; they obtained five paleoshoreline positions (Figure
3.12). Schaetzl et al. (2002) correlated the highest bluff (242.0 m: SID307) with

Main Lake Algonquin, a lower observation (236.3 m: SID302) with the Ardtrea

84

phase, and three lower observations (~228.0 m: SID301, 305 and 306) with the
Wyebridge phase. They claim paleoshorelines in the vicinity of Mackinac Island

correlate well with those near the center of Deane’s (1950) study area.

Lake
Huron

%

LII/((3 Slrails of

M a (‘/\' i II a (‘

Nfichigan

 

 

Figure 3.12: Relict bluff sites at Mackinac Island. Sites are labeled with a unique
site identification number and an elevation value (e. g., 642: 200 m).

Although two paleoshorelines at Mackinac Island apparently share
elevations with others located at Wyebridge, Ontrario, Schaetzl et al. (2002) did

not apply Stanley or Deane’s typology consistently to a third. For example, the

85

Nipissing plane at Mackinac Island occurs at ~193 m (634 ft) and seems to
correspond with Goldthwait (1910) and Stanley’s (1936) Nipissing shoreline at
Wyebridge, Ontario (194 m, 637 ft). Mackinac bluffs stranded at ~228.0 m (750 ft)
have elevations that correspond with Stanley’s (1936) Wyebridge bluff at
Wyebridge. But Schaetzl’s highest feature (242.0 m: SID307), which they
associated with the Main phase, does not correlate with Stanley and Goldthwait’s
Main elevation at Wyebridge (256 m, 840 ft) -- a difference of nearly 14 meters.
Therefore, either the highest bluff at Mackinac Island was either last cut by a
lower water level, or lower features at Mackinac Island are not correlated with
those at Wyebridge, Ontario.

The highest bluff at Mackinac Island has long been identified as belonging
to the Main phase of glacial Lake Algonquin (Stanley, 1945; Schaetzl et al., 2002),
so I continue to recognize this association. The next lower bluff rests 5-6 m lower
than the Main bluff, which is typical of Ardtrea bluffs located near Orillia,
Ontario, so I continue to recognize this association. I am compelled, however, to
reject the Wyebridge correlation Schaetzl et al. (2002) made with features
stranded at 228 m. Conspicuous examples of Upper Orillia shorelines and few
instances of Wyebridge shorelines are present at Sault Ste. Marie, Cockburn
Island, the Munuscong Islands, the Penetang Peninsula, or in Lake Simcoe
District, so it seems unlikely that Wyebridge shorelines would be expressed
better at Mackinac Island than those carved elsewhere, or expressed stronger

than those carved by the Upper Orillia water plane. So, in light of the elevations

86

and relative strengths of Upper Orillia shorelines elsewhere, and the relative
location of Mackinac Island with respect to these Upper Orillia shoreline
features, I correlate features at ~228 m on Mackinac Island with the Upper Orillia

phase of glacial Lake Algonquin and not with the Wyebridge phase.

Table 3.6: Approximate elevations of glacial Lake Algonquin water planes
measured at Mackinac Island, Michigan.

Approximate elevation (r11 Water plane / lake phase

 

242 Main
236 Ardtrea
228 Upper Orillia
? Lower (observed but not surveyed)

 

The Douglas Lake area, Michigan

Schaetzl et al. (2002:406) began classifying their shoreline data near
Douglas Lake and the University of Michigan Biological Station in Cheboygan
County, MI ”because only two highly distinct shorelines exist in this region.”
According to their work, and their interpretation of Leverett and Taylor’s (1915)
previous work, relict shorelines of the Main phase of glacial Lake Algonquin are
expected at the 225 m elevation plane and remnants of a lower and later
shoreline are expected at ~210 m. Interestingly, Spurr and Zumberge (1956) also
argue that two distinct shorelines exist in this region; they accept the Main phase
at 738 ft (225 m) but claim residual segments of a pre-Algonquin shoreline are
stranded at 724 ft (220 m). Spurr and Zumberge (1956) make no mention of a

post-Main shoreline at 210 m. Obviously, these reports differ in their

87

interpretations. I am disinclined to accept Spurr and Zumberge’s (1956) pre-
Algonquin lower shoreline hypothesis, however, because I expect that any
feature composed of unconsolidated sediments (as are the ones in question)
would have been buried, reshaped or reworked under the high waters of the
relatively long-standing Main phase. Also, the idea that drowned shorelines
simply re-emerged unscathed after several hundred years of subaqueous
exposure, especially in an environment that suffered ”the long fetch afforded by
Lake Algonquin” and ”frequent and intense cyclonic storms” (Krist and Schaetzl,
2001:14), seems unreasonable.

Before conducting fieldwork, I reviewed Schaetzl's data and plotted them
on the Pellston, Indianville, and Mullet Lake MI 7.5 minute USGS topographic
map sheets. Of the thirteen points they surveyed in this area, four have elevation
values near 230 m, six have values near 225 m, one at 221 m, and two others at
~211 m. Given the 3-meter limit of precision I have adopted during this work,
the differences among these elevation values suggest that four, not two,
distinctive water levels existed in this region.

I revisited field sites at locations around Douglas Lake and surveyed other
relict shorelines nearby (Figure 3.13). I started at the boat ramp located due
south of Pells Island and traveled counterclockwise around the upland known as
Pellston Island. In SEi Sec. 30 T37N R3W, I measured the gravel lag at the base
of a protruding relict bluff at 222.2 m (SID180). I then followed the base of the

upland as it crosses over the Pellston Island spit (Krist and Schaetzl, 2001) and

88

then south and down into SE34- Sec. 25 T37N R4W; where I measured the base of a
relict bluff at 223.0 m (SID181). I continued southward and surveyed several
positions along the west side of the island (unfortunately, most of these points
were later discarded because each sample contained large anomalies, thus
indicating the nearby tree stands or the intermittent snowfalls of the week
perturbed GPS signal reception). In NE% SW% Sec. 7 T36N R3W, the base of a
stranded bluff rests at 223.0 m (SID182). Schaetzl et al. (2002) measured a 221.6
m elevation at a location 1 km east of this point and along the same feature
(SID328). The apparent difference in elevation between these two samples (~1.4
m) is less than the critical threshold value (3.0 m) used to distinguish distinctive
lake levels, so they are considered to represent that same water plane.

I was able to observe several remnants of what I assume to be lower and
later shorelines as I traveled around the north end of Burt Lake. For example, as
Indian Road approaches Burt Lake, several houses are situated along a bluff cut
at 187.6 m (SID184), which Spurr and Zumberge (1956:102) might associate with
the Nipissing Great Lakes. On the east side of Burt Lake, a pipeline runs north-
south through Sec. 12 T36N R3W and crosses two apparent shorelines.
Admittedly, the bluffs here are weak but they are discernible. The higher bluff
was measured at 211.8 m (SID185) and the lower at 197.0 m (SID186).

Returning to Douglas Lake, starting at South Fish Tail Bay (NE % Sec. 33
T37N R3W) and working westward, a single relict shoreline and bluff can be

traced along and above the southern rim of Douglas Lake. I found an instance of

89

a double bluff near Grapevine Point, which is located due north of the University
of Michigan Biological Station campus (Sec. 28 T37N R3W). Figure 2 in Spurr
and Zumberge (1956) illustrates the feature. The base of the lower bluff is cut at
220.3 m (SID179), which is 3 m higher than the average water level of Douglas

Lake. The base of the upper bluff rests at 227.4 m (SID178).

 

,333:226.1m

 

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469227.4in.468;231.2m .
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Figure 3.13: Relict bluff sites in the Douglas Lake area. Sites are labeled with a
unique site identification number and an elevation value (e.g., 642: 200 m).

90

I surveyed other relict bluffs north of Douglas Lake (e.g., NW of North
Fishtail Bay in Sec. 22 T37N R3W and SE of Lancaster Lake in Sec. 8 of the same
township), but had to discard these samples because they contain highly
scattered position data. My field notes indicate a heavy snow / rain mix was
falling during data collection, so it is likely that precipitation interfered with GPS
signal transmissions as water collected atop the antenna.

Given the complex glacial history of this former ice-marginal region
(Blewett, 1995; Spurr and Zumberge, 1956), it comes as little surprise that so
many different relict features over a relatively wide range of elevations exhibit
the erosive influences of water. I believe, however, that there is evidence to

support six distinctive water levels (see Table 3.7) in this area.

Table 3.7: Approximate elevations of glacial Lake Algonquin water planes and
the N ipissing water plane measured in the Douglas Lake area.

Approximate elevation (m) Water plane / lake phase

 

 

230 Ice-contact margin?
225 Main
221 Ardtrea
212 Upper Orillia
- Lower Orillia
197 Uncertain
188 Nipissing

 

As mentioned above, I reviewed Schaetzl’s data for this region and found
4 points with elevation values near 230 m (e. g., SID327), which is 5 meters higher

than the generally accepted elevation (~225 m) of the Main phase (Spurr and

91

Zumberge, 1956; Schaetzl et al., 2002). Features at this elevation might mark an
ice-contact margin described by Spurr and Zumberge (1956). I removed these
points from the glacial Lake Algonquin dataset and placed them into the
supplemental dataset. Among the areas covered by the Pellston, Indianville, and
Mullet Lake, MI topographic map sheets, 8 samples now mark relict bluffs along
the 225 m elevation plane. Given the long history of associating features at this
elevation to the Main phase of glacial Lake Algonquin, I am compelled to do the
same. Smaller sets of lower shoreline relicts are associated with later and lower
glacial Lake Algonquin lake phases as indicated in Table 3.7; the lowest position

is associated with the Nipissing Great Lakes.

Beaver Island, Michigan

Beaver Island is a part of Charlevoix County, Michigan. It is situated
among a small group of islands in Lake Michigan, approximately 50 km north-
northwest of the City of Charlevoix and 55 km west of Mackinac City. Leverett
and Taylor (1915:425) described an upland area on Beaver Island as a ”morainic
tract about 4 miles long from northeast to southwest and 1% miles wide” with
altitudes ”considerably above the highest Algonquin beach.” The authors
explored ”unusually well developed” (p.425) beaches on the north, south and
west sides of this upland; they make no mention, however, of any relict coastal

landforms on the eastern side of Beaver Island.

92

Dietrich (1978) visited Beaver Island fifty years later, examined soils and
landforms around Leverett and Taylor’s (1915:425) ”morainic tract” and found
features that ”appear to be beach gravels that are well below what are generally
recognized as Lake Algonquin levels” (p.287). He reasoned these beach gravels
might belong to later and lower glacial Lake Algonquin lake phases because they
occur at elevations higher than the expected Nipissing water plane.

Furthermore, he claimed the most substantial bluff features, particularly those
situated on the southern and western sides of the relict upland, were eroded by
Lake Nipissing and not by Lake Algonquin - as Leverett and Taylor (1915)
claimed. Dietrich (1978) continued to argue that ” the island’s only prominent
wave-cut scarp attributable to Lake Algonquin” exists on the eastern side of the
island ”between Iron Ore Bay and Miller Marsh" (p.287). He also speculated that
two small inland lakes (Fox Lake and Green’s Lake) existed as bays in glacial
Lake Algonquin. According to Dietrich’s (1978) interpretation of Leverett and
Taylor’s (1915zp439) isobase map, the highest glacial Lake Algonquin water plane
intersects the contemporary land surface between the 215 and 230 m planes of
elevation. The highest elevation on the island surface is approximately 245 m, so
it is possible that a proto-Beaver Island existed as an island in glacial Lake
Algonquin. The apparent conflicts between claims made about the relationship
between the highest Lake Algonquin water plane and the locations of relict
lacustrine features on Beaver Island prompted me to visit the Island and examine

these features.

93

I conducted fieldwork on Beaver Island, Michigan during late October,
2003 (Figure 3.14). I used the Beaver Island North and Beaver Island South 7.5
minute USGS topographic maps and The Wojan-Cashman Map of Beaver Island
(Cashman and Wojan, 1977) as field guides. The provisional USGS maps provide
good hypsometric information, but the topology of the local road network is
better represented by the Wojan-Cashman Map. The morainic tract is situated in

the southern half of the modern island.

Michigan

BeaVe‘r'
Island ‘ ;,
62:229.,3m f" , '
, 0915922232111
_. 1 53160325111qu ,
'_ .i’163:229.0m.

 

Figure 3.14: Relict bluff sites on Beaver Island, Michigan. Sites are labeled with
a unique site identification number and an elevation value (e.g., 642: 200 m).

94

I selected an initial set of twelve potential bluff targets, which includes
only those locations with elevations above the expected Nipissing water plane
(189 m after Dietrich, 1978). Unfortunately, none of the maps I used illustrates
the actual state of land ownership fragmentation or the maze of private in-
holdings that exists within the Jordan River State Forest. Many in-holdings are
fenced, gated and padlocked, so access to relict features on these properties is
prohibited without permission. I was able to contact several landowners and
obtain permissions to access their lands, but was unable to secure enough
permissions to visit all potential bluff targets.

Mr. Larry Dawson owns property (Sec. 29 T38N R10W) that abuts
Leverett and Taylor’s (1915:425) ”morainic tract.” A moderate bluff (~6 m high)
is cut into the northern side of the tract. No other feature is higher at this
location. I sampled soil at the top of the bluff and found red-brown till with
coarse gravel. Sampling at the base of the bluff, however, revealed a thin layer of
organic material and colluvium (~10 cm) over a thicker layer of beach sand (~1
m). The juxtaposition of soil samples taken at such proximate locations suggests
this bluff marks the highest remnant shoreline on Beaver Island. A buried lag of
small rounded gravel rests within the layer of beach sand at 229.3 m (SID162),
which is approximately 6 In higher than the highest shoreline that Dietrich (1978)
measured.

I followed the bluff eastwardly and down into a wetland where it loses its

distinctive toe. I continued to follow the upland tract around the southern rim of

95

Fox Lake where I found a second wave-cut bluff at 223.2 m (SID159). The
elevation of this feature is similar to the highest elevation that Dietrich (1978)
reported and is approximately 2 meters higher than the average water level of
Fox Lake (as indicated on USGS tOpographic maps). The near coincidence
between bluff and lake elevations is, perhaps, the reason why Dietrich (1978)
speculated Fox Lake once existed as a bay in glacial Lake Algonquin. Sampling
at this location again revealed red-brown till at the bluff top and beach sand at
the bluff base. The lower relict shoreline lost its distinctive character and graded
into a wetland as I traveled southeasterly along the upland tract. I could not
distinguish the higher shoreline feature (229.3 m) anywhere along the southern
rim of Fox Lake.

About 1.2 km farther east, the lower shoreline regains its character in the
form of a very large bluff (~15 m). Sampling at the top of the bluff revealed red-
brown till composed mainly of sand with some gravel. Large boulders are
scattered across the surface of the bluff top. Soil sampling at the base of the bluff
(SID160: 225.1 m) revealed a layer of plant detritus, which rests over a layer of
peat, which rests over a layer of beach sand. An apparent relict bar sits 50 m
”lakeward” of the relict bluff, which may have acted as a barrier between open
water and a lagoon that allowed the peat to form.

Vegetation is dense and the ground is very wet along the base of the large
bluff. So, I retreated uphill to a trail that parallels the bluff top and continued

eastward. After another kilometer or so I left the trail and followed the morainic

96

tract as it turns south. A few hundred meters farther, I found a conspicuous
wave-cut bluff cut into the eastern side of the morainic tract at 229.0 m (SID163).
Beyond this site the bluff loses its distinctive toe, vegetation becomes denser and
the ground gets wetter. I assume this feature is correlated with the high feature I
found on Mr. Dawson’s property. I could not distinguish lower shoreline
features at this site.

The eastern flank of the morainic tract is very difficult to approach from
the northern end. I attempted to follow the Dotty Trail as marked on the Wojan-
Cashman Map of Beaver Island (Cashman and Wojan, 1977), but found the path
flooded and impassible. The western flank is also very difficult to approach
because almost every access road is gated and locked, or posted with a hostile
message for potential trespassers. Lacking permission, I did not search for relict
shoreline features along these two flanks.

The eastern and western flanks of the morainic tract converge toward the
southern end of proto—Beaver Island, but the tip of the tract has apparently been
truncated by Nipissing waters (Dietrich, 1978). I visited the prominent Lake
Algonquin scarp Dietrich (1978) described along the eastern side and ”between
Iron Ore Bay and Miller Marsh” (p.287) and measured three elevations along
one-kilometer of its length (214.0 [SID165], 212.5 [SID161] and 211.4 m [SID164]).
Each value is within 3 m of each other, so all are considered marks along one
relict shoreline. In my opinion, this feature serves to distinguish a third and

lower Algonquin water plane at Beaver Island.

97

As a final note, the supposed morainic tract changes character halfway
along its 8 km length; rough hills typical of the northern 5 kilometers give way to
a relatively smooth surface typical of the southern 3 kilometers. As mentioned
above, soil samples taken above the highest shoreline in the northern zone
yielded red-brown tills with gravels. Sediments sampled along the smooth
surface near the southern edge, however, did not reveal a red-brown till, but a
sequence of well-sorted sands and gravels. A gravel pit at the southern tip of the

upland reveals a profile of sorted sediments (Figure 3.15).

 

Figure 3.15: Exposed sediment profile in a gravel pit located near the southern
end of proto-Beaver Island. A 2-foot carpenter’s level is shown for scale.

In my opinion, the apparent differences (i.e., topographic expression and general
sediment structure) between the northern and southern zones of the central

upland on Beaver Island indicate the two zones were shaped by different

98

processes. Also, the elevation of the land surface above the gravel pit (at 220 m)
is lower than the two highest shoreline elevations I measured at the north end of
the upland (at ~229.0 m), so it seems reasonable to suggest the southern zone of
the upland was formed, or at least shaped, under lake waters.

I measured relict shoreline features at three distinct levels of elevation on
Beaver Island, MI (see Table 3.8). The highest shoreline, which is displayed best
at Mr. Dawson’s property, is correlated with the Main phase of glacial Lake
Algonquin. Paleoshoreline elevations at Beaver Island correlate well with others
stranded nearby on Leverett and Taylor’s (1915) Brutus Island (Schaetzl etal.,
2002). Evidence of other water planes exists at Beaver Island, particularly along
the eastern and western flanks of the central upland, but the beach gravels
Dietrich (1978) described are beyond the scope of this research. I believe much

more can be learned from further study at Beaver Island.

Table 3.8: Approximate elevations of glacial Lake Algonquin water planes
measured at Beaver Island, Michigan.

Approximate elevation (m) Water plane / Lake phase

 

229 Main
223 Ardtrea
212 Wyebridge

 

From Petoskey to Traverse City, Michigan
The area between Petoskey and Traverse City, MI contains many upland

areas that contain long and narrow lakes (e.g., Lake Charlevoix and Walloon,

99

Intermediate and Torch Lakes). The terrain is complex and relatively difficult to
interpret. Leverett and Taylor (19152426) speculated glacial Lake Algonquin
”probably” extended up these valleys and left ”distinct shorelines around Pine
Lake” (now called Lake Charlevoix - see Figure 3.16) that ”mark the highest
Algonquin beach and some lower members of the upper group.” The authors

also mentioned relict features at ”Undine and Hortons [sic] Bay” (Leverett and

Taylor, 1915: 426).

 

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# 1695213: . 12.. 3 , 1,;
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lg; J.

 

 

Figure 3.16: Relict bluff sites near Petoskey, Michigan. Sites are labeled with a
unique site identification number and an elevation value (e. g., 642: 200 m).

100

A high bluff parallels the southern limit of Little Traverse Bay west of
Petoskey. I studied three sites near Bay Shore and along Pincherry Road
(SID108, 109 and 110). All three have ~213 m elevations. This shoreline is the
highest in the region and, according to Spurr and Zumberge (1956: Figure 2), it
represents the Main phase. I do not agree with this correlation, however, and
attribute it to the Ardtrea phase instead. I considered the well known instance of
a Main phase bluff that is situated along the north shore of Little Traverse Bay.
Leverett and Taylor (1915:424) describe ”the best-preserved parts” of ”the upper
group of Algonquin beaches” between Middle Village and Canby, MI. And, I
considered that Schaetzl et a1. (2002) measured bluff elevations at two sites near
Good Hart, M1: the highest was at 224.4 m (SID313), which they attributed to the
Main phase; and the lower one at 221.8 m (SID314), which they attributed to the
Ardtrea phase. These features are well preserved (pers. obs.), where not
interrupted by the N ipissing transgression and can be traced confidently for
fifteen kilometers to Harbor Springs. A site situated approximately 4 km west of
Harbor Springs marks the Main plane at 222.4 m (SID315); another situated 4 km
west marks the Ardtrea plane at 215.9 m (SID316). Supposed ”Main” shorelines
at Bay Shore and Harbor Springs have elevations that differ by 9.4 m but are
separated by no more than 10.5 km, thus implying a rate of uplift near 0.9 m / km.
An uplift rate as large as 0.9 m/ km is not expected at this location or latitude
and, if proposed, would imply some kind of geologic unconformity exists.

Lacking evidence of any such unconformity, I do not carry the Main phase across

101

Little Traverse Bay. Instead, I carry only the Ardtrea phase, which implies a 0.2
m/ km rate uplift. Although such a correlation might seem provocative, I am not
the first to propose it. Larsen (1987) summarized ”a lack of consistency between
the [Michigan and Huron] basins, indicating that the [Main] Algonquin level of
Michigan is considered younger than that of Lake Huron” (p20).

Between the Undine Cemetery and Horton Bay (SEi Sec. 1 T33N R7W), I
measured a well-defined instance of a Nipissing shoreline; a small bluff is cut at
186.3 m (SID113), situated a few hundred meters north of Lake Charlevoix (not
shown in Figure 3.16). Goldthwait (1910: Figure 4) reported a Nipissing
elevation of 613 ft (186.8 m) near Burgess, MI, which is located only a few miles
away.

Many houses along Boyne City Road in Horton Bay are built into a high
bluff. For example, at Mr. Jim Chellis’ property (SE% NEi Sec. 6 T33N R6W), I
measured the old shoreline at 208.4 m (SID112). This shoreline is the highest
apparent shoreline in the region and I correlate it with the Upper Orillia.

The Horton Bay area exhibits several intermediate shorelines situated between
the high bluff at Mr. Chellis’ property and the current water level of Lake
Charlevoix. These features are represented by a series of beach ridges that are
stranded along what once was a low-gradient shorezone. These intermediate
shoreline features were not surveyed because beach ridges are not always stable

indicators of former water level elevations.

102

Leverett and Taylor (1915: 426) claimed glacial Lake Algonquin once
covered ”Grass, Clam, Torchlight and Elk lakes to the basin of Grand Traverse
Bay” (T orchlight Lake is now known as Torch Lake). They offered, however,

only one description of a relict landform:

A mile and a half south of Elk Rapids the upper beach is marked by
a strong gravel ridge and a hooked spit, and one or two of the
members below it are faintly developed. It runs thence south close
to the shore of East Arm, much of the way as a wave-cut bench and
bluff, in which form it passes south into swampy flats (Leverett and

Taylor, 1915:426).

These features are clearly illustrated on the Elk Rapids, MI and Williamsburg, MI
7.5 minute USGS topographic map sheets. Plotted contour lines indicate,
however, that these features occur at elevations near 185 m, which is lower than
expectations of glacial Lake Algonquin water levels but consistent with
expectations of Nipissing water levels. Field observations confirm the elevations.

Further review of the topographic maps prompted me to inquire about
other features in the area - particularly those situated along Torch Lake. For
example, just north of French Point (Sec. 18 T29N R8W), I observed what I
believe to be a set of two relict shorelines as indicated by a double bluff. The
lower shoreline is situated at 185.5 m (SID119), which I correlate with the

Nipissing Great Lakes. The higher bluff is situated at 193.6 m (SID117 and 118).

103

I traced the higher bluff both northwardly and southwardly and looked for other
conspicuous instances to sample. Most of the land area along Torch Lake has
been disturbed by residential and seasonal home development, which rendered
several observable instances unsuitable for sampling. I did, however, find one
instance situated on a vacant lot that had only been staked for development.
Here, a relict shoreline is marked by a substantial bluff at 192.2 m (SID116). I
found no evidence of higher or lower Algonquin water levels around Torch Lake
and remain uncertain about which phase of glacial Lake Algonquin, if any, these

points are associated with. So, I placed them into the supplemental database.

The Leelanau Peninsula, Michigan

Leverett and Taylor (1915) indicated the Algonquin beach is well—defined
along the Leelanau Peninsula of Michigan. They identified a relict islet near
Omena, a high lake cliff near Northport and several sets of lower Lake
Algonquin beach ridges among several other locations. More recently, Kincare
and Larson (2002) mapped the surficial geology of Northern Leelanau Peninsula
and provisionally marked the locations of the uppermost Algonquin shoreline.
The authors claim ”isostatic uplift has elevated Algonquin shorelines from about
197 meters (646 ft) in Leland to just over 200 meters (656 ft) near Lighthouse
Point.” They did not, however, find any evidence of ”lower Algonquin strands.”
Instead, Kincare and Larson (2002) suggest that the low strands that do exist

likely belong to the Algoma and Nipissing Great Lakes.

104

I investigated sites described by Leverett and Taylor (1915) and mapped
by Kincare and Larson (2002). Figure 3.17 show the area. The upper Algonquin
water plane and the later Nipissing Water plane are expected to be separated by
less than 20 meters of elevation. In some locations, the higher and older
shoreline was obviously cut away by transgression of the lower. In other
locations, both relict shorelines have been cut away by recent wave action and

substantial bluffs now mark the contemporary shoreline.

Grand Tram: rse

B a y

 

 

Figure 3.17: Relict bluff sites on the Leelanau Peninsula. Sites are labeled with a
unique site identification number and an elevation value (e.g., 642: 200 m).

105

In Sec. 15 T30N R11W, I measured the base of a strong wave-cut bluff at
199.5 m (SID101); it is the highest wave-cut feature in the area. As the ground
slopes away from the bluff and toward Suttons Bay it exhibits a sequence of
minor ridges and terraces. The ridges run parallel to each other and the modern
shoreline. While these ridges and terraces may represent agricultural
modifications, they may, rather, represent relict beach ridges associated with
falling water levels. Additional study is needed. A small orchard is situated at
the site and trees have been planted along these terraces.

In SW% Sec. 35 T31N R11W, Freeland Road switches direction to ascend a
steep bluff. Kincare and Larson (2002) indicate the Algonquin shoreline occurs
here. A gravel lag is buried at the base of the bluff and rests at 199.3 m (SID102).
Incidentally, this site is one of the last sites along the Leelanau Peninsula that
remains forested, wet, and undeveloped for residential or seasonal home uses.

I visited the knoll Leverett and Taylor (1915) described east of Omena.
While the authors suggested several lower Algonquin members are exhibited
here, my observations indicate only one high and conspicuous shoreline is
present; it has been truncated by the N ipissing shoreline in two places. I found
no evidence of any higher, lower or intermediate shorelines situated around the
knoll. I surveyed the northeast side of the knoll and the uppermost shoreline
was cut at 196.9 m (SID103); the Nipissing shoreline is at ~186 m (SID119).

Michigan Route 22 approaches a glacial Lake Algonquin bluff about two

km north of Omena. The relict shoreline rests at 196.4 m (SID104).

106

Leverett and Taylor (1915) described the highest Algonquin beach as it
”turns directly west across the peninsula about a mile north of Northport"
(p.426). I visited this area and believe their description is not correct. Although
the Algonquin bluff does begin to turn west north of N orthport, it does not
proceed directly across the peninsula. Rather, the shoreline traces the back of a
small bay (Kincare and Larson, 2002) and returns east just north of Garthes Pond.
From Garthes Pond, I observed the bluff to head in a northeasterly direction for
another 2.2 km. It is from here that the shoreline turns west and across the
peninsula. A Lake Algonquin shoreline is marked at 198.0 m (SID105) by a
massive bluff near Christmas Cove (Sec. 21 T32N R11W). The bluff has been
truncated by the contemporary shoreline of Lake Michigan. I did not find lower
shorelines below the massive bluff and above the Nipissing water plane.

The high truncated bluff reappears south of Christmas Cove and near the
Onominese Cemetery (Sec. 5 T31N R11W). I measured the shoreline and it is cut
at 201.0 m (SID106). This site is cluttered by gravelly colluvium in many places
below the steep bluff face, so this elevation is considered high.

As mentioned above, Kincare and Larson (2002) indicate the Algonquin
shoreline is situated at ”about 197 meters (646 ft) in Leland.” I observed the base
of a wave-cut bluff at 194.2 m (SID107: 637 ft) approximately two km east of
Leland and near the eastern shore of Lake Leelanau (SW% SW% Sec. 11 T30N
R12W). This feature is well-defined for about one km (near Wardens Point) and

sheltered from westerly winds.

107

Prom Mullet Lake to Alpena, Michigan

Schaetzl et al. (2002) followed Leverett and Taylor’s (1915) descriptions of
relict landforms and surveyed many in the area around Black Lake (Figure 3.18).
Most have elevations that correspond with others located in the Douglas Lake
area. Each water plane tends to decline as one travels south toward Alpena.
Such correspondence is expected given that paleoshorelines are oriented parallel

to the generally presumed isobase of isostatic rebound (after Hough, 1958).

 

   
 

 

      
 

 

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Figure 3.18: Relict bluff sites in the Black Lake area. Sites are labeled with a
unique site identification number and an elevation value (e.g., 642: 200 m).

108

The highest paleoshoreline (227 - 222 m) is conspicuous and easily associated
with Main Algonquin. A few instances of a slightly lower water plane are
associated with the Ardtrea phase (222 — 217 m). In keeping with my recognition
of Orillia water planes in Ontario and elsewhere in Michigan, I am compelled to

update several sites that had been attributed to the lower Wyebridge phase

(5113399, 410).

    
      
 

.3702206.5m
.334:210.4m

335:519’6m'
.418:193.9m

7 , 420:201;6m ' '
.,,._ - 421:221.6m‘.

 

 

 

 

Figure 3.19: Relict bluff sites in the Long Lake area. Sites are labeled with a
unique site identification number and an elevation value (e.g., 642: 200 m).

109

Schaetzl et al. (2002) also surveyed features in the area around Long Lake
(Figure 3.19). The authors attributed a single instance of a very low
paleoshoreline (201.6 m: SID420) with the Payette phase (Figure 3.19), but I do
not agree with this correlation. Interpretation of Karrow (1987, Figure 5) and
Stanley (1936: Figure 2) indicates the Payette water plane is expected to dip
below the N ipissing water plane well before it reaches the contemporary
Michigan shore; consequently, Payette shorelines are not expected to exist
landward of Alpena, MI. So, the instance of a very low paleoshoreline must

represent a water plane higher than the Payette water plane.

From Alpena to the Au Sable River, Michigan

The Thunder Bay River area represents a conspicuous break between sets
of paleoshorelines stranded north and south of Alpena (Figure 3.20). Leverett
and Taylor (1915) expressed great difficulty regarding their attempts to identify
distinctive water planes along the flat and sandy terrain, and to connect these
two sets. Also, Schaetzl et al. (2002: Figure 4a, p411) show their statistical model
of the Main Algonquin water plane did not perform well in this region (as
expressed by relatively large positive residuals). The Thunder Bay River area
seems to present the same problem I encountered at Little Traverse Bay: if the
nearest highest feature to the south is associated with the nearest feature
attributed to the Main phase, then the local linear rate of uplift between the two

sites is surprisingly high. Perhaps this is no coincidence.

110

 

' 410:2142
m Lake
Huron

 

Th 21 11 d e r
B a .1/

p 25*;
{4 :l‘21‘lzgmys5a1asm
‘ 43020936111 '

 

 

Figure 3.20: Relict bluff sites near Alpena, Michigan. Sites are labeled with a
unique site identification number and an elevation value (e. g., 642: 200 m).

I think it is reasonable to speculate that features situated south of Alpena,
having been worked by several converging water planes, might not express the
elevation of the first water level to act upon it. Therefore, Main Lake Algonquin
features may not be present here. As best as I can determine, only two sites
south of Alpena express Main Lake Algonquin (214 m: SID431, 435). The
balance, I believe, are associated with the Ardtrea and Upper Orillia water

planes. Paleoshorelines situated near Harrisville, between Alpena and the Au

111

    

  

Sable River, have elevations that correspond very closely with others located

south of Little Traverse Bay (Figure 3.21).

 

'lz: him/'11

’
lit/tr

I. a It 13
H 1.1 r a II

 

 

 

Figure 3.21: Relict bluff sites near Harrisville, Michigan. Sites are labeled with a
unique site identification number and an elevation value (e. g., 642: 200 m).

From Au Sable River to Saganing, Michigan
The area between the Au Sable River and Saganing, MI is generally
composed of fine lucustrine materials (Farrand and Bell, 1982) and exhibits a

topography that is generally flat or slightly rolling. Two instances of end

112

moraines composed of fine-textured till can be found near Turner and Tawas
City (Farrand and Bell, 1982), however, fewer instances of conspicuous wave-cut
bluffs can be found within the region.

Leverett and Taylor (1915: p.419) described a discontinuous beach ridge,
which they characterize as the main Lake Algonquin ridge, that begins near a
cemetery in Bay City, ”passes about 1% miles southeast of Omer” and ”runs
about a mile back from the lake [i.e., Lake Huron] northward to Alabaster, in
Iosco County.” They also described a ”lake cliff and upper ridge” that crosses
the Au Sable River ”4 miles west of Oscoda” (p.420).

Recent editions of 7.5 minute USGS topographic maps indicate the
features mentioned by Leverett and Taylor (1915) and situated between Bay City
and Alabaster have an approximate present-day elevation of 184 m, which
coincides with the expected N ipissing water plane at these locations (Goldthwait,
1910). Field observations confirm this elevation. Therefore, these relict features
were likely last shaped by post-glacial Nipissing waters and not by Lake
Algonquin waters.

Leverett and Taylor’s (1915zp420) lake cliff, however, is well-defined on
the Foote Site Village 7.5 minute USGS topographic map and rests at present-day
elevations greater than 190 m, which is higher than the expected N ipissing plane
at this location (Goldthwait, 1910). Burgis (1977) describes the same shore-cliff in
terms of a graded deltaic sequence that formed in relatively high lake waters (she

suggests Lakes Grassmere and Lundy) and was later truncated by glacial Lake

113

Algonquin waters. She also illustrates a lower delta (Burgis, 1977; Figure 44) that
formed at the former mouth of the Au Sable River and in glacial Lake Algonquin
waters. Burgis (1977) did not provide elevation data for these features.

Old logging roads provide access to the truncated delta, a portion of
which rests in the Au Sable State Forest, north of the Au Sable River, and west of
Oscoda, Michigan (Figure 3.22). I made observations along the base of a very
strong bluff in Sections 26, 23, 14 and 11 of T24N R8E. For example, in NW} NE%

Sec. 26, the bluff is approximately 30 m high, well-preserved and steep.

I... a It 1:
H u. r 0 u

.....

      
  

1.3: :11- , F 'f a..." _.A_ r 4121196109?" .
. i *5 11221399311139 , > .

g; , it...” ~ v..,.,.z_,..,r
. “gas-”lags! g

   
 

, 71221936111 v. . V.

 

Figure 3.22: Relict bluff sites near Oscoda, Michigan. Sites are labeled with a
unique site identification number and an elevation value (e.g., 642: 200 m).

Schaetzl et al. (2002) reported an elevation of 196.0 m (SID412) along the
base of this bluff at a location just north of Bissonette Road (SW1? NEl: Sec. 26). I
report elevation values of 196.3 m (SID124: SE1: SWi Sec. 26) and 196.8 m

(SID125: NWi N132} Sec. 26). As one proceeds northward into Sections 23 and 14,

however, the bluff degrades into a series of benches. Two upper benches are

114

backed by faint scarps with basal elevations at 211.4 m (SID996) and 204.3 m
(SID995). The lowest portion descends into a swamp and no conspicuous wave-
cut features can be identified along its slope. The upper bench positions, which
are not associated with conspicuous wave-cut bluffs, are retained in the
supplemental database.

South of the Au Sable River in Sec. 10 of T23N R8E, I made observations
along the bases of a weak scarp (SID999: 203.0 m - not shown), a strong scarp
(SID122: 196.5 m) and a conspicuous wave-cut bluff (SID123: 193.4 m) roughly 6
m high. The two later observations were made along the same feature but at
locations separated by 530 m. At this time, I cannot explain the apparent large
difference in elevation (~3.0 m) between two instances of the same feature.
Additional sampling and, perhaps, a rigorous examination of soil stratigraphy at
these locations may yield some explanation. Yet, because the later two
observations are associated with a conspicuous bluff feature, their positions are
included in the shoreline dataset - as is the uncertainty that exists between them.
The highest of the three positions, which is not associated with a conspicuous
bluff feature, is retained in the supplemental database.

Given the substantial relief of this bluff (~30 m) and the coincidental
higher elevations of scarps found at locations both north (204.3 m) and south
(203.2 m) of the Au Sable River, the base of this bluff (~196 m) is likely not
correlated with the highest Algonquin water level, but a subsequent and lower

one. I associate the base of this bluff with the Upper Orillia water plane.

115

Summary

I described the methods I used to collect relict shoreline data and
substantially improve the glacial Lake Algonquin dataset created by Schaetzl et
al. (2002). I surveyed 88 new relict features in Northern Michigan and Western
Ontario and was able to attribute 69 features to known glacial Lake Algonquin
lake phases; the balance is reserved in the supplemental database.

I retained 128 of the 146 positions Schaetzl et al. (2002) collected. Four
elevations taken near Douglas Lake, Michigan, mark anomalous features that
rest higher than the Main water plane (~225 m). The other fourteen points not
retained were taken from features that resemble offshore bars, barrier bars, or
spits and, so, were not collected according to my sampling protocol; I reserve
these eighteen points in the supplemental database and they await future review.
Also, many of the elevation values I obtained at sites in the Munuscong Islands
region, near Douglas Lake and near the Au Sable River compliment the elevation
values reported previously by Schaetzl et al. (2002) - so it seems our efforts
identified the same features and obtained similar elevation values from them.

I conflated well-known paleoshoreline data taken by others at Sault Ste.
Marie (10) and St. Joseph Island (19). Together, the glacial Lake Algonquin
dataset and the supplemental database hold 243 bluff records; Appendix A
presents a complete list of them; Figure 6.10 shows bluff locations with respect to
predicted shorelines. Individually, each sample marks a point along a former

shoreline of glacial Lake Algonquin (although a few mark N ipissing shorelines).

116

In aggregate, they outline several distinct water planes within the region of
interest: Main (57), Ardtrea (41), Upper Orillia (33), Lower Orillia (16),
Wyebridge (12), Penetang (13), Cedar Point (17), Payette (7), Sheguiandah (3),
Korah (1) and others (43). Apparent differences among water plane elevations
are useful for modeling the cumulative effects of differential isostatic rebound
(Chapter 5).

A major difference exists between the method Schaetzl et al. (2002) used to
correlate paleoshorelines with named water planes, and the method I used.
Schaetzl et al. (2002) began correlating shoreline data and Lake Algonquin lake
phases in the Douglas Lake area, worked their way east and west, and then
proceeded north and south. I attempted to follow that procedure, but
encountered difficulties when attempting to recognize their set of four lake levels
at locations north of the Straits of Mackinac - where additional water planes are
clearly evident. Ultimately, I started again but began correlating paleoshoreline
data with Lake Algonquin lake phases at Sault Ste. Marie instead. Sly and Lewis
(1972), Cowan (1985), and Karrow (1987) correlated features in the region with
respect to the Lake Algonquin lake phases named by Deane (1950: The Upper
Group containing the Ardtrea, Upper Orillia and Lower Orillia phases), Stanley
(1936: The Lower Group containing the Wyebridge, Penetang, Cedar Point and
Payette phases) and Hough (1958: Sheguiandah and Korah), so it was relatively
easy to interpret my results at Cockburn Island in terms of their findings.

Having recognized the connections Cowan (1985) made between Manitoulin

117

Island and Sault Ste. Marie, and the apparent connections that I recognize
between Cockburn Island and St. Joseph Island, it became clear that relict
features in Michigan’s Upper Peninsula needed to be reclassified. From these
northern locations I then progressed southwestwardly and continued to
recognize water planes as I went.

Relict shoreline features at Cockburn Island are particularly important
features because they add much needed support near the northern rims of glacial
Lake Algonquin water planes. They also provide clues about former ice margin
position (Karrow, 1987). We know that the Superior Lobe of the Laurentide ice
sheet retreated northeastwardly after reaching a maximum extent that covered
the northern portion of Michigan’s Lower Peninsula (Karrow, 1987; Larson and
Schaetzl, 2001). Lakes in the Michigan and Huron basins were joined when
retreating ice uncovered the Indian River lowlands and, slightly later, the Straits
of Mackinac, which Larsen places at approximately 11,200 yr BP (after Hansel et
al., 1985). Water levels in glacial Lake Chicago dropped to the glacial Lake
Algonquin level upon joining (Hansel et al., 1985), which left the outlet at
Chicago abandoned (Larson and Schaetzl, 2001) and directed all outflow to the
Fenelon Falls outlets near Kirkfield, Ontario (Finamore, 1985). Thus began the
Main phase of glacial Lake Algonquin. The presence of Main phase shorelines
on Cockburn Island suggests that the ice sheet retreated through Cockburn
Island sometime during the early portion of this lake phase; early enough to

allow bluff cutting and other shoreline development processes to occur. Karrow

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(1987) concluded that St. Joseph Island was deglaciated ”about 11,000 yr BP or
shortly thereafter” (p119). Cockburn Island is apparently situated along the
same isobase that runs through St. Joseph Island (Figure 3.8), so both islands
were likely deglaciated at the same time. Therefore, locations between the Straits
of Mackinac and the Cockburn Island-St Joseph Island region must have been
deglaciated within, roughly, a ZOO-year period.2 Main phase and lower
shorelines on Cockburn Island tell us that Cockburn Island was deglaciated
before the Fossmill outlets at North Bay, Ontario, because lower lake phases are
associated with falling water levels brought about by deglaciation of the outlets
at North Bay (Kaszycki, 1985; Karrow, 1987). Karrow et a1. (1975) reported
radiocarbon dates that indicate glacial Lake Algonquin, from the Main phase to
the lowest, existed between 11,200 yr BP and 10,400 yr BP. Relict shoreline
features at Cockburn Island are important features because they help to place the
ice sheet margin as well as the northern extent Main Lake Algonquin into a

spatial context within this very short time frame.

 

2 Karrow (1987) mapped a separation between areas of the Laurentide ice sheet that are
known as Superior ice and Algoma ice (Figure 2, page 114). Superior ice covered the
Straits of Mackinac and Algoma ice covered St. Joseph Island and Cockburn Island. This
separation complicates the deglaciation history of the northern Lake Huron basin and
precludes, for now, speculation about how glacial ice retreated in locations between the

Straits of Mackinac and the St. Joseph-Cockburn Islands region.

119

Understanding the relict features at Mackinac Island remains a key to
establishing the proper link between the Upper Peninsula and the Lower
Peninsula- interpretation of these features, however, remains a crux. Proto-
Mackinac Island was small and distant from other Algonquin islands, and it
holds relatively few conspicuous paleoshorelines to study (despite their
notoriety). Schaetzl et al. (2002) correlated features at 242 m with the Main
phase, those at 236 m with the Ardtrea phase, and those at 228 m with the
Wyebridge phase; they claimed features at Mackinac Island have elevations
similar to others in the Lake Simcoe District of Ontario (Deane, 1950). I was
compelled, however, to reinterpret these data as I attempted to integrate new
data with old findings. I reviewed Deane’s (1950) work and consider the work of
Cowan (1985) and Karrow (1987), as well as my own, and found reasons to
believe that features Schaetzl et al. (2002) correlated with the Wyebridge phase
rest at elevations better correlated with the earlier Upper Orillia water plane. For
example, I considered Deane’s (1950) descriptions of features; he characterized
Upper Orillia bluffs as strong and characterized Wyebridge features as ”not
strong” and indicative of ”only a short pause of Lake Algonquin at this level”
(Deane, 1950: 174). I considered my work at Cockburn Island — the strongest
bluffs there occur at elevations that correlate very well with the Upper Orillia
water plane and rest at elevations higher than the expected Wyebridge water
plane. Also, I did not find features on Cockburn Island that were associated with

the Wyebridge water plane. Finally, I considered the relative location of

120

Mackinac Island with respect to other places that mark the Upper Orillia water
plane. Ultimately, I correlated features at ~228 m on Mackinac Island with the
Upper Orillia phase of glacial Lake Algonquin and not with the Wyebridge
phase. More study is needed here.

Making correlations between relict shoreline features and Lake Algonquin
lake phases is difficult in areas near Little Traverse Bay (Lake Michigan) and
Thunder Bay (Lake Huron) because paleoshorelines in these areas are oriented
roughly north-south, and interrupted by contemporary water features that are
oriented roughly east-west. Ever since Leverett and Taylor (1915), the highest
paleoshorelines on either side of these water features have been considered as
representatives of the same water level - Main Lake Algonquin. Such
connections, however, implicitly require anomalous crustal deformations to have
occurred in both bays. In Emmet County, for example, the highest
paleoshoreline cut into the north side of Levering Island occurs at 232 m and the
highest paleoshoreline cut into the south side of Brutus Island (on the north side
of Little Traverse Bay) is 222 m; both shorelines are associated with the Main
phase (Leverett and Taylor, 1915; Schaetzl et al., 2002). These two sites are
separated by approximately 30 km, thus yielding a reasonable 0.33 m/ km linear
rate of elevation change along the Main water plane. Continuing southwardly, if
we assume the highest paleoshoreline on the north side of Little Traverse Bay is
the same as the highest paleoshoreline on the south side of Little Traverse Bay,

then that would require an effective 0.90 m / km linear rate of change along the

121

water plane over a mere 10.5 km span. In other words, assuming the highest
paleoshoreline on both sides of Little Traverse Bay are the same shorelines would
require an anomaly in the isostatic rebound process at this location. A similar
anomaly is required if the highest paleoshorelines north and south of the
Thunder Bay River are also considered as the same. Lacking any knowledge of
anomalous deformations in these two areas, I must consider that the highest
paleoshorelines situated north of Little Traverse Bay / Alpena are not correlated
with the highest paleoshorelines south of Little Traverse Bay / Alpena.

In related work, Goldthwait (1910) described features along the highest
paleoshoreline in the area between Kincardine and Port Elgin, Ontario. He also
reported several features occur at anomalously low elevations. Karrow (1988)
surveyed this region and found that features previously identified as the highest
Lake Algonquin shoreline had actually been eroded and lowered by later water
levels. Consequently, the features in question indicate the action of younger lake
phases and not the Main phase of glacial Lake Algonquin. I speculate that a
similar pattern of erosion occurred in the areas south of Little Traverse Bay and
Thunder Bay, Michigan. Both Deane (1950) and Schaetzl et al. (2002) reported
Main and Ardtrea water planes seem to converge at roughly this latitude, so it is
quite reasonable to speculate that later, lower, and converging water planes
continued to erode bluffs that might have once held marks of the Main phase,
but no longer do. The Main Lake Algonquin water plane elevation at Port Elgin,

Ontario (220 m after Karrow, 1988: p159) correlates well with highest

122

paleoshoreline found north of Alpena and west of Long Lake (221.6 m). The
elevations of lower relict features situated south of Port Elgin, Ontario (208 m
after Karrow, 1988: p159) correlate well with features situated south of Alpena,
Michigan (209 m). In both cases, however, the elevations of lower relict features
correlate best with the younger Upper Orillia lake phase and not the higher and
older Main or Ardtrea phases.

Karrow (1987) and Larsen (1987) have noted the long-standing
controversy regarding whether certain water planes in the Lake Algonquin series
are parallel, thus implicating changes in outlets were responsible for changes in
water levels, or whether they converge toward a single outlet, which would
implicate isostatic rebound as the sole cause of shoreline deformation. Stanley
(1936) and Hough (1958) suggested the shorelines were parallel; each
represented a new outlet. Deane (1950) and Schaetzl et al. (2002), however,
found evidence of convergence between the Main and Ardtrea water planes;
each shoreline represented differential uplift relative to the same (also uplifting)
outlet. Larsen (1987) argued for convergence after considering historic uplift
data (Clark and Persoage, 1970). This work finds some evidence of both.

Like Dean (1950) and Schaetzl et al. (2002), this study finds evidence of
convergence between the Main and Ardtrea water planes. Proceeding roughly
southwardly: Main and Ardtrea bluffs at Cockburn Island are vertically
separated by approximately 8 m (280 and 272 m, respectively); in the Munuscong

Islands region they are separated by ~7 m (265 and 258 m, respectively); on

123

Mackinac Island they are separated by ~6 m (242 and 236 m, respectively); and,
in the Douglas Lake area, they are separated by ~4 m (225 and 221 m,
respectively). Moreover, the Main and Ardtrea shorelines are difficult to
differentiate at locations south of Little Traverse Bay (Lake Michigan) and
Thunder Bay (Lake Huron) because they either occur within 3 m of each other or
they were reworked or destroyed by younger and lower lake phases.
Convergence between the Main and Ardtrea shorelines suggests differential
uplift relative to the Fenelon Falls outlet was the cause of deformation and tilt
during the Main and Ardtrea phases.

Upper Orillia shorelines consistently occur below Ardtrea shorelines at
Cockburn Island, the Munuscong Islands, Mackinac Island, and in the Douglas
Lake area, but elevation differences between them provide conflicting evidence
regarding convergence. Between some locations they appear to converge toward
the south, while among other locations there is evidence of parallelism.

Few sites exist that mark multiple instances of later and lower water
planes. Cockburn Island and the Munuscong Islands region, for example, are the
only two locations that hold instances of both the Upper Orillia and Penetang
shorelines. The vertical difference between these shorelines at Cockburn Island
is 36 m, whereas the difference in the Munuscong Islands region is only 30m. A
decreasing separating distance with decreasing latitude suggests convergence
again, hence the influence of differential rebound. A comparison between two

points, however, is not sufficient for characterizing the spatial patterns of two

124

regional water planes, so no valid conclusion can yet be drawn about the
relationship between the Upper Orillia and Penetang water planes.

Evidence of convergence or parallelism between particular water planes in
northern parts of the Huron basin notwithstanding, these data cannot be used to
resolve the question of where Lake Algonquin stood in the southern parts of the
Huron and Michigan basins. Like Schaetzl et al. (2002), my study area did not
extend into those areas.

The new elements of the glacial Lake Algonquin dataset, including those
surveyed during this work (n=69) or conflated from previous work (n=29), fill
large data gaps (Cowan, 1985) and furnish new points of support for the

restoration of glacial Lake Algonquin water planes (Taylor, 1895).

125

CHAPTER 4: ACCURACY ASSESSMENTS

Introduction

All spatial data are, to some extent, contaminated by error (Foody, 2003;
Burrough and McDonnell, 1998; Heuvelink and Burrough, 1993; Openshaw, 1989
and Goodchild and Gopal, 1989). Error implies a discrepancy between an
attribute of an entity or phenomenon and its measured representation. A
potential danger exists in work that uses spatial data because errors can
propagate through analyses, render results uncertain and prompt misleading
interpretations (Shortridge, 2001; Heuvelink, 1988). Heuvelink and Burrough
(2002: 111) have argued the importance of knowing ”how accurate the data
contained within spatial databases really are” so the ”value of the derived
information” might be known. Accordingly, the accuracies of the datasets
employed in this work need to be assessed so that knowledge about data errors
can be used to improve data analysis and qualify the results.

I report exploratory data analyses and accuracy assessments of the
paleoshoreline dataset and a selected portion of the National Elevation Dataset
(NED: Gesch et al., 2002). I use the public-domain R environment for statistical
computing and graphics (R Development Core Team, 2005), particularly the geoR
(Ribeiro Jr. and Diggle, 2001), gstat (Pebesma 2004), maptools (Bivand, 2005), and
RandomFields (Schlather, 2001) packages, to explore and analyze data and

conduct statistical tests.

126

Two datasets

I employ two datasets: a) a primary set of paleoshoreline positions; and b)
a secondary digital elevation model that covers the region of interest. Every
elevation value in each dataset, however, is the result of a random measurement
process and likely contains error. From the outset I expected errors in elevation
to have much greater potentials for contributing uncertainty to spatial model
results than errors in horizontal locations because a significant difference in scale
exists between the horizontal and vertical dimensions that bound glacial Lake
Algonquin shorelines. The region of interest (see Figure 1) includes the
confluence of Lakes Michigan and Huron and it extends northward past Sault
Ste. Marie, Ontario, southward to the Au Sable River, westward to the Leelanau
Peninsula and eastward to Harrisville, MI. The north-south dimension of the
study area covers approximately 240 km of terrain whereas the east-west
dimension covers 195 km. If a paleoshoreline position was to contain a
horizontal location error of 10 m, then the error magnitude would represent no
more than 0.005% of the east-west extent or 0.004% of the north-south extent. In
other words, the relative size of a 10-meter horizontal error would be very small,
and if input to a spatial model, then its influence on model results would also be
small. I chose the GPS leveling methods and equipment described in Chapter 3
because they typically yield horizontal coordinates with sub-meter errors. A
sub-meter error is an order of magnitude less than a 10-meter error, so its relative

influence is expected to be negligible.

127

The contemporary range of elevations associated with stranded glacial
Lake Algonquin features (~133 m) is much smaller than either range of
horizontal coordinate values, which is the important difference in scale
mentioned above.1 Consider a paleoshoreline position that contains a 10 m
elevation error, rather than a horizontal error. A 10-meter error in elevation
would represent 7.5% of the elevation range. Hypothetically, if a 10-meter
elevation error were entered into a spatial model, then it would likely perturb
results. By comparison, the relative impact of a 10-meter error in elevation is
much greater than the impact of a 10-meter horizontal error given the substantial
difference between vertical and horizontal extents. Moreover, the contemporary
ranges of elevation associated with individual glacial Lake Algonquin water
planes are less than 133 m, so individual water-plane models supported by such
erroneous positions are subject to even greater impacts and uncertainties. 2 That
is why I used differential GPS technology and designed a strict sampling

protocol that limited data collection activities to occur only during temporal

 

1 The average level of water in the contemporary Michigan-Huron basin is 176 m, below
which glacial Lake Algonquin shorelines cannot be observed. The highest elevation
associated with a glacial Lake Algonquin feature is approximately 309 m (Cowan, 1985).
2 Schaetzl et al. (2002: Table 4, p412) reported three post-Main Lake Algonquin water
plane elevations at Alpena, MI and Sault Ste. Marie, Ontario. The differentially warped
Ardtrea, Wyebridge and Payette water planes include elevations that range 75, 77 and 51

meters, respectively, between the two sites.

128

windows that framed optimal satellite constellation geometries suitable for the
taking of accurate and precise elevation measurements. Differential GPS
technology can yield elevations with sub-meter accuracy when used properly.
Yet, proper planning and use notwithstanding, it is common knowledge among
the GPS community that GPS technology resolves elevation values less precisely
than horizontal coordinate values. So, the set of GPS-measured paleoshoreline
data, particularly the set of elevation values, might contain errors that need
mitigation. I focus my attention on these. And, it is common knowledge that
”elevations recorded within digital models are fraught with errors” (Fisher,

1998:215), so I also focus on them.

Assessment of the glacial Lake Algonquin dataset

The task of assessing accuracy is concerned with describing errors in data
(Shortridge, 2001). Typical assessments begin with the assumption that each
error is the result of a random measurement process, proceed by comparing a set
of measured values to a set of known or higher-order values assumed to be
accurate, and end with a description of the distribution of error. A higher-
quality paleoshoreline dataset does not exist to assess the set of data collected
during this work. Yet, rather than assume paleoshoreline data are accurate by
virtue of being the highest-order available, I attempt an assessment by
recognizing potential sources of error and conceptually or empirically estimating

their potential values. Each shoreline sample is subject to two sources of error: a)

129

the limits of precision associated with the method I used to select relict shorelines
in the field; and b) the limits of precision associated with the methods I
employed to measure and process shoreline positions at selected sites. I address

both.

Analysis of potential selection errors

As explained in Chapter 2, I rely on the gravel lags that form at the bases
of wave-cut bluffs to be the set of best indicators of former water-level positions.
Morton and Speed (1998) suggest the precision with which a lake level can be
established by the elevation of a wave-cut bluff alone is sub-meter, but my
knowledge of contemporary water-level behavior suggests the precision might
be as great as three meters (see Chapter 2). Such imprecision is supported by
Goldthwait (1910: Figure 2) who, when drafting profiles of uplifted water planes,
used bands ”6 feet broad according to the vertical scale” to represent ”small scale
discordances as must be expected because of the original variation” (p37) in
water plane heights.

Every field site, save the few noted otherwise, exhibited a conspicuous
gravel lag from which the limits of long-term wave-action can be inferred fairly
confidently. A possibility exists, however, for some gravel lags to have been
deposited at elevations higher than long-term water levels (e.g., during storm
events). If I selected such a feature, then a probability exists for the selected

elevation to overestimate the former water level. I expect such errors are rare.

130

Based on my experience in the field and following the research of others (e. g.,
Goldthwait, 1910; Morton and Speed, 1998), I expect most selection errors to be 0
m, the majority of selection error values to fall within the interval of 0 and 1 m,

and, on rare occasions, extreme values to fall within the interval of 1 and 3 m.

Ground control

Measurement errors in the paleoshoreline dataset cannot be assessed
directly because no paleoshoreline surveyed in this work has been surveyed
independently or by higher-order methods; an indirect assessment method is
needed. So, I assess the precision of the data collection and processing methods,
from which I infer the accuracy of data they yield. Small sets of National
Geodetic Survey (NGS) bench marks were measured during each field campaign.
The protocol used to measure and process paleoshoreline position data was used
to measure and process bench mark data. After each campaign, each set of bench
marks was added to the pool of ground control data. Calculated discrepancies
between measured and actual bench mark positions are used to assess the
accuracy of paleoshoreline position data and correct any bias.

The National Geodetic Survey is the authority for determining latitude,
longitude, elevation, crustal velocity and gravity throughout the United States
and it serves as the depository for geodetic data of the highest-order (NGS, 1998).
Geodetic data represent a network of precisely surveyed control stations with

accurate position attributes (Bossler, 1984). Horizontal control stations, also

131

known as monuments, are established to provide users with accurate longitude
and latitude values. Vertical control stations, also known as bench marks, are
established to provide accurate height (elevation) information. Interestingly, not
all bench marks have horizontal data of geodetic-quality and not all monuments
have height data of geodetic-quality, but some do have both. The NGS maintains
a geodetic datasheet (NGS, 2004) for each monument and bench mark.
Datasheets are archived annually on a regional basis and those that represent
control stations in Michigan were last archived in November, 2004. Datasheets
contained within this archive are used to assess the precision of the data
collection methods described in Chapter 3 and to assess, by inference, the
accuracy of paleoshoreline position data.

Twenty-four different NGS control stations (see Table 4.1) were occupied
and measured during my field campaigns, of which ten stations have geodetic
longitude and latitude information. During data processing, however, I
discovered six station samples to be unfit for use. Three samples (PIDs OJ0706,
PK0154 and PK0165) were collected on November 13, 2003 and each contains
conspicuous large errors - particularly station PK0154. Such large errors
prompted me to review all field notes, field equipment and data processing
methods, but I found nothing from these sources to help me explain their
occurrences. I discovered, ultimately, the US Coast Guard archive of GPS Status
Message Reports (US Coast Guard Navigation Center, 2004), which contains

historic status information about the GPS space and control segments.

132

Table 4.1: Vertical differences between measured and published heights.
NGS bench marks are indicated by their Permanent Identifiers (PIDs).

Observations used to assess shoreline elevation data.

 

GPS height NGS height Difference
PID (m) (m) (m)
N F0260 259.86 260.26 -0.40
PK0227 193.85 194.28 -0.43
PL0361 192.20 192.21 -0.01
PL0369 190.63 190.61 0.02
PL0370 195.62 195.83 -0.21
PL0389 182.93 182.36 0.57
QJ0086 180.31 179.70 0.61
QJ0151 198.21 196.51 1.70
QK0087 185.55 184.84 0.71
QK0325 255.22 255.55 -0.33
QK0410 177.29 177.56 -0.27
QK0469 194.63 194.52 0.11
QK0470 205.24 206.60 -1.36
QK0484 232.83 232.04 0.79
RJ0161 193.20 192.37 0.83
RJ023O 236.24 234.77 1.47
RJ0644 208.01 208.49 -0.48
RJ0691 234.17 234.68 -0.51
Observations perverted by satellite malfunction (rejected).
OJ0706 183.32 184.72 -1.40
PK0165 203.88 206.02 -2.14
PK0154 185.28 190.66 -5.38

Observations taken at bench marks with non-geodetic quality

height information (rejected).

QK0852 243.16 242.00 1.16
* 267.97 266.70 1.27
* 249.40 248.41 0.99

 

Several GPS status reports (USCG, 2004) revealed that a GPS satellite
malfunctioned on November 13, 2003 and was broadcasting bad data for at least

twenty-four hours. The GPS signal was eventually turned off, but not before I

133

collected data. I discarded these samples because I could not remove the
influences of bad data obtained from the now decommissioned satellite. This
event prompted me to review every archived status report for each day data
collection activities occurred, which included the previous work accomplished
by Schaetzl et al. (2002). Fortunately, I found no evidence to suggest other bench
marks or any paleoshoreline data should be discarded for similar reasons.

I rejected three more control station samples because each was obtained at
a site having non-geodetic quality information. For example, the datasheet that
represents bench mark QK0852 contains elevation data not obtained by rigorous
survey, but interpolated from an old topographic map built using the obsolete
North American Vertical Datum of 1929 (N AVD29). Unfortunately, this mark is
the only documented vertical control station on Beaver Island, MI. I rejected two
marks collected by Schaetzl et al., 2002 (marked in Table 4.1 with an asterisk - *)
because they were taken at road intersections annotated with spot heights on
topographic maps (and rounded to the nearest foot), and not at bench marks
with high-order geodetic information. The lesser-qualities of these three control
points are insufficient for assessing the greater precision of GPS-based

measurement methods or the accuracy of the data they yield, so they are rejected.

Analysis of measurement errors
Differences between measured and published elevations are listed in

Table 4.1 for eighteen bench marks having geodetic-quality height information.

134

Summary statistics (Table 4.2) and a stem-and-leaf plot (Figure 4.1a) show
measurement errors are small in magnitude; the distribution appears symmetric

and centered near zero.

Table 4.2: Summary statistics that describe the set of differences between
measured and published bench mark elevations.

Sample statistics Value Test for mean at 0 Value
n 18
minimum -1.36 m
median 0.00 m

mean (bias) 0.16 m matched-pairs t p = 0.4010
standard error of mean 0.19 m
standard deviation 0.77 m
maximum 1.70 m

 

 

 

2
-3 i, 1
-2 E
3
-1 4 c. 0
-0 55443320 ‘2;
0 0166788 E
1 57 in" ’1
2
3 -2
-2 -1 0 1 2
Quantiles of a Normal Distribution
(6) (b)

Figure 4.1: Distribution of error in sampled bench mark elevations: a) Stern and
leaf plot - solid line denotes the decimal place; and b) q-q plot of standardized
errors with a one-to—one line and 90% confidence envelope.

135

Results of a matched-pairs t test indicate the mean difference between
measured and published elevations (0.16 m) is not statistically different than zero
at the 90% confidence level. A q-q plot of standardized error values (Figure 4.1b)
and results of a Shapiro-Wilk test for normality (a = 0.10: W=0.9540 and p =
0.4915) provide no significant evidence to suggest the sample distribution of
elevation error does not fit a Normal distribution. No elevation difference
exceeds 1.7 m, which is less than the three-meter threshold used to distinguish
different long-term water levels. As expected, the majority of measured
elevations (15 of 18, or 83%) contain sub-meter errors.

I used scatterplots to examine associations between error and position
(Figures 4.2 and 4.3). I used Kendall’s non-parametric tau statistic to test the
strengths of associations because latitude and longitude values are non-linear
measures of distance. Kendall's tau does not rely on assumptions about the
underlying distribution of data. It is applied to the ranks of data (which
mitigates the non-linear distance problem) and takes values ranging between -1
and +1 (which can be interpreted like Pearson’s or Spearman’s statistics). No
plot or statistical test result provides strong evidence to suggest errors, either

signed or unsigned, are associated with location or elevation.

136

 

 

 

2
A 1 ..
g 515'
B 0 4‘. ,
t: .. «r a
LU -1 .
-2
-3
180 200 220 240 260
Actual elevation (m)
(a)
3 3
2 s 2 , a
a " as
g 33 I' '3' ‘P \E’ {5 {E are
E 0 . £1 “#4' “Iii-I. 3 E 0 $5 ilk—hi IIIII I?
LL! _1 LU -1
T g: {3:
-2 -2
-3 -3
-86.0 -85.0 -84.0 -83.0 44.0 45.0 46.0 47.0
Longitude (dd) Latitude (dd)
0)) (C)

Figure 4.2: Scatterplots of signed error in sampled bench mark elevations and

position. Errors and elevations are reported in meters. Latitude and Longitude
values are reported in decimal degrees.

137

3.0

 

 

 

:5: 2.5
{‘3’ 2.0
g, 1.5 .4 as
(D
E 1.0 -.
e 1:: «ft?
m 0.5 I” '13 q” 4,
0.0 i
180 200 220 240 260
Actual elevation (m)
(a)
3.0. 3.0
E 2.5-: E 2.5-
% 2.0 8 2.0
3 . :5 .
(U i (U ' ‘
E 1.0 ,. E 1.0
9 - z... 33 1": .3; e .. a: g :1:
a; 0.5: ; t...” a. Lil-J 0.5 .. f s
0.0: 1+ 0.0 is i“
-86.0 -85.0 -s4.0 -83.0 44.0 45.0 46.0 47.0
Longitude (dd) Latitude (dd)
0?) (C)

Figure 4.3: Scatterplots of unsigned error in sampled bench mark elevations and
position. Errors and elevations are reported in meters. Latitude and Longitude
values are reported in decimal degrees.

I used Moran’s I statistic (Bailey and Gatrell, 1995: 270) to test for spatial
autocorrelation. The calculated statistics for signed and unsigned errors (I =

0.047 and -0.090, respectively) are near zero and indicate no spatial

138

autocorrelation is present, so I infer no spatial structure exists among the errors

in these bench mark elevations.

Table 4.3: Results of Kendall’s non-parametric tests for associations between
position and elevation error.

 

Signed error Unsigned error
tau p value tau p value
Longitude 0.150 0.410 0.294 0.096
Latitude 0.072 0.709 0.268 0.131
Elevation -0.163 0.369 0.137 0.454

 

The actual distribution of error is not known, but sampled errors appear
small, random, normally-distributed and not a function of location, elevation or
autocorrelation. Because the methods used to measure paleoshoreline elevations
are the same as those used to measure bench mark elevations, errors in
paleoshoreline elevations are inferred to be similarly small, random, normally
distributed and spatially unstructured.

Calculated differences between measured and published latitude and
longitude values (converted to meters) are listed in Table 4.4 for seven
monuments having geodetic-quality latitude and longitude information (recall
that ten were measured but three were rejected because of a satellite
malfunction). All location coordinates contain sub-meter errors. On average, a

measured location is typically within 0.5 m of the actual location.

139

Table 4.4: Horizontal differences between measured and published N GS
benchmark locations.

 

Error in Error in
PID Latitude (m) Longitude (m) Distance (m)
NF0260 0.16 0.09 0.19
PL0361 -0.47 0.22 0.52
QK0325 -0.96 0.19 0.98
QK0469 -0.48 -0.41 0.63
QK0470 -0.65 -0.02 0.65
QK0484 -0.30 0.30 0.42
R]0161 -0.03 0.21 0.21

 

The methods used to measure paleoshoreline locations are the same as

those used to measure bench mark locations, so horizontal errors in

paleoshoreline locations are inferred to be similarly small. Moreover, the

maximum error observed in horizontal coordinate data (0.98 m at mark QK0325)

is smaller than the widths of most gravel lags that form along contemporary

Great Lakes shorelines (pers. obs.). From this observation, and given the large

extent of the study area, random and small horizontal errors likely associated

with measured shorelines, while likely not zero, are hereafter considered to be

not meaningfully different than zero. In short, they are ignored.

Cumulative elevation errors in paleoshoreline data

Recall that each shoreline measurement is subject to two sources of error:

a) the limits of precision associated with the method I used to select relict

shorelines in the field; and b) the limits of precision associated with the methods

I employed to measure and process shoreline positions. I have no reason to believe

that either one of these sources of error can be influenced by the presence,
location, magnitude or direction of the other, so I assume that each error process
operates independently of the other. Therefore, the total error in any
paleoshoreline elevation is expected to be the simple sum of selection and
random measurement errors. I describe in Chapter 5 the process I used to

estimate total elevation error in my paleoshoreline elevation data.

141

Assessment of the National Elevation Dataset

The National Elevation Dataset (Gesch et al., 2002) is a digital elevation
model (DEM) that provides seamless data coverage of the United States. It is
produced by the US Geological Survey (USGS) and distributed in raster format.
The NED represents bare earth elevations and is the best such dataset available
for the area under investigation. Unlike older DEMs (e. g., the USGS 7.5-minute
and 3 arc-second models) that contain elevation data tied to different spatial
reference systems, the NED contains elevations that are referenced only to the
North American Datum of 1983 (NAD1983) and North American Vertical Datum
of 1988 (NAVD88) -- and they share a common unit of measure (meter). NED
elevations are arranged on a grid and spaced at one arc-second intervals, which,
at 46° N latitude, spans approximately 31 meters in the north/ south direction
and 22 meters in the east/ west direction. When first released, most NED
elevations were derived from reprocessed versions of older DEMs, but
increasingly they are being derived from new and more accurate source
materials. The NED is now assembled completely from 10-meter and 30-meter
resolution sources and new tiles at 10-meter resolution are incorporated as they
are produced (Gesch et al., 2001). The NED is updated every two months; this
work employs the December 2004 release that contains new elevation data for a

portion of northern Lower Michigan.

142

DEMs contain errors in elevation that are the cumulative results of
imprecise sampling, measurement and interpolation processes (see e.g.,
Shortridge, 2001; Fisher, 1998; Bolstad and Stowe, 1994; Brown and Bara, 1994
and Shearer, 1990). 3 The NED has not yet been assessed for accuracy, but
according to the USGS (2005), ”a plan for assessing the overall accuracy of the
National Elevation Dataset (NED) based on independent high-accuracy geodetic
control is currently under development.” The USGS (2005) suggests NED users
should consult ” published information on the accuracy of the source digital
elevation models (DEM's) from which NED was assembled.”

Spatial metadata distributed with NED data contain polygons that outline
footprints of source DBMS and attribute tables with statistical summaries of
error. A root mean square error (RMSE) quantifies the average mismatch
between a small set of ground-based and DEM—reported elevations within each
footprint. Such values are not specific to particular locations and hence cannot
be used to pinpoint spots where elevations can be considered as reliable or in
need of improvement (Shortridge, 2001; Kyriakidis et al., 1999). Furthermore,

RMSE values represent mismatches calculated prior to NED processing, which

 

3 Horizontal locations stored in a digital elevation model are controlled during the
production process (i.e., they are selected and not measured), so digital elevation models
by design do not contain horizontal errors (Maune, 1996). Admittedly, it is possible for
an elevation to be assigned incorrectly to a location, but such violations still are

considered elevation errors and not horizontal errors.

143

may be different than actual values. The NED data processing protocol includes:
a) the application of large filters to remove production artifacts or smooth
discontinuities along input tile boundaries; b) bilinear interpolation methods that
coerce data from extant resolutions into available spots along the arc second grid;
and c) geodetic transformations that change elevations formerly rounded and
stored as integers (either in feet or meters) into decimal meters stored with
floating point precision (USGS, 2005). Consequently, a potential mismatch exists
between metadata-reported and actual RMSE values. So, while historic RMSE
values associated with source files may be the best available indicators of
accuracy, actual accuracy is uncertain.

The NED also contains elevation data for Canada that are situated near
the US/ Canada border and within the one-degree tile structure employed by the
USGS (Gesch et al., 2001; Gesch et al., 2002). Canadian elevation data were not
collected according to USGS protocols, but likely derived from the Digital
Terrain Elevation Dataset (DTED: NIMA, USGS and NGDC, 1997). The DTED
was created for large areas of the world by the former Defense Mapping Agency
during the 19605 and 19705, and used primarily for military purposes. NED
metadata provide scant information about how these data were collected or
processed, but metadata-reported RMSE values (10 - 29 m) indicate elevation
data for Canada contain large errors relative to those associated with other
sources (RMSE 1 - 7 m). Consequently, elevation data for Canada are considered

a likely source of uncertainty in model results.

144

Geoprocessing the NED

NED data were projected onto the Michigan GEOREF planar coordinate
grid and resampled to 45-meter resolution using GIS software. I was initially
reluctant to reduce the horizontal precision of NED data, but was compelled by
computer memory and storage limits (NED data for the study area consume
nearly 0.5 GB of disk space at 30-m resolution). Nevertheless, the new resolution
is an improvement over the coarser 90—m data employed in related work by
Schaetzl et al. (2002) and Drzyzga et a1. (2002). Also, many grid cells associated
with Lakes Michigan, Huron and Superior were masked from analysis because
they do not represent land surface information. The geoprocessed version of
NED data is hereafter referred to as, simply, ” the DEM.”

I divided the DEM into three subsets: Lower Peninsula, Upper Peninsula,
and Ontario. I divided Michigan data into two subsets because elevation data for
the selected portion of the Lower Peninsula were derived primarily from contour
lines on topographic maps, and most elevation data for the selected portion of
the Upper Peninsula were derived photogrammetrically. Elevation data for
Ontario were derived differently than elevation data for Michigan, so I suspected
internal inconsistencies might differ as well. The literature has long recognized
that differences among DEM production methods yield DEMs with different
error characteristics (e. g., Wood, 1996 or Brown and Bara, 1994), so I sought to
examine each subset to ascertain whether or not such differences existed wihin

my data. I originally considered subsetting the DEM using source tile polygons

145

that were attributed with different production method data, but doing so would
have fragmented the study area into many non-contiguous and hard-to-manage
units. More importantly, however, the USGS can update any or all data within a
source tile with elevations obtained via methods not consistent with those
reported in the spatial metadata file (USGS, 2005). Consequently, footprints of
NED source tiles, which indicate the extents of pre-NED production methods,
may not coincide with the extents of actual production methods. This
complicating factor prompted me to use simple majorities to inform my choice of

three subsets.

Hypsometric analysis

Initial assessment of the DEM and each subset can be achieved by visual
analysis of frequency histograms, which can reveal internal inconsistencies if any
are present (Hutchinson and Gallant, 2000; Wood, 1996). The frequency
distribution of my DEM elevations (Figure 4.4a) is skewed toward lower
elevations and it contains several conspicuous spikes. The largest spike is
situated between 176 and 181 m and represents a large number of ”water” cells
associated with the contemporary Lake Michigan-Huron water plane that remain
in the model, as well as others associated with inland lakes Burt, Charlevoix and
Mullet. A secondary peak is situated between 213 and 218 m and associated with
large homogenous groups of cells that represent the elevations of Hubbard Lake

(Lower Peninsula) and North Manistique Lake, Manistique Lake and South

146

Manistique Lake (Upper Peninsula). Several lesser spikes are also evident at 213,
244, 274 and 305 m, but these cannot be explained by known topographic
regularities.

The Lower Peninsula subset is the largest of the three and its distribution
(Figure 4.4b) dominates the distribution of the whole DEM as the two histograms
are quite similar. High frequencies of 213, 244, 274 and 305 m elevations in the
DEM are not evident in this subset. Other and lesser spikes, however, appear at
three-meter intervals. Most 1:24,000 USGS topographic maps have elevation
contours mapped at ten-foot intervals (roughly three meters), so it seems that
artifacts associated with DEM production methods that utilized digitized
contour lines have survived geoprocessing and are observable.

The Upper Peninsula histogram (Figure 4.4c) contains many low
elevations that represent the characteristic lake plain topography of the area, and
a small peak centered near 255 m, which represents several bedrock uplands.
Two conspicuous spikes occur at 177 and 217 m: the lower is associated with
”water” grid cells representing contemporary Great Lakes water level elevations;
the higher is associated with a large number of small inland lakes that occur at
various locations across the lake plain of the eastern Upper Peninsula. The Seney
National Wildlife Area, for example, is predominantly swampland and most
open water bodies situated within it were mapped with the same elevation

value.

147

120

   

   

73 70‘ 100
O O
O O
2 e 80
6 6 60
C C
9 3 40
a a
t: if: 20
O
200 300 400 500 200 300 400 500
Elevation (m) Elevation (m)
(a) the DEM (b) Lower Peninsula subset
120' 120
13 100 13 100
O O
8 8 '
5 803 5 80 l
3 60 3 601 i 5 .
g g l a .
j J l
E} 40 E} 40 . i f
“.3 93 l
u. 20 u. 20 '
0‘ 0
200 300 400 500 200 300 400 500
Elevation (m) Elevation (m)
(c) Upper Peninsula subset ((1) Ontario subset

Figure 4.4: Frequency histograms of elevation. Bin width is one meter.

Large spikes at 213, 244, 274 and 305 m in the DEM histogram are not evident in
the Upper Peninsula histogram. Yet, other and lesser spikes do appear at three-

meter intervals. The majority of elevation data in this subset were derived

148

photogrammetrically yet some were derived from contours, which explains the
consistent pattern of overrepresented elevations at three-meter intervals.

The Ontario subset (Figure 4.4d) is the smallest of the three but contains
the full range of elevation values. Topography in the Ontario region is
interesting and unique because it contains both stranded lake plains and a high
and exposed portion of the Canadian Shield. Yet, irregular Shield topography
does not account for the regular spikes that occur at 213, 244, 274 and 305 m or
the intermediate spikes at 229, 259, and 289 m. When meters are converted to
imperial feet, these spikes reveal a consistent pattern of overrepresented
elevations at 100 and 50 ft intervals, respectively, and suggest a systematic and
non-topographic cause (Hutchinson and Gallant, 2000; Wood, 1996). Given that
1:250,000 USGS topographic maps of the region were drafted using a 50-foot
contour interval, it seems reasonable to speculate that such mapped contours
were used as source materials for DTED elevations, which are the likely sources
of NED elevations in Ontario. Again, NED metadata contain no information
about the sources used to assemble data for locations in Ontario, so this is only
speculation. Regardless of source, however, spikes in Ontario elevation data
betray a likely artifact of a DEM production process and they indicate the

elevation model over-represents contour elevations within this region.

149

Ground control

The task of assessing accuracy is concerned with describing errors in data
(Shortridge, 2001). Typical assessments: begin with the assumption that each
error is the result of a random measurement process; proceed by comparing a set
of measured values to a set of known or higher-order values assumed to be
accurate; and end with a description of the error distribution. I assembled a pool
of high-order check points consisting of National Geodetic Survey (NGS) and
Geodetic Division of Canada (GDC) control stations. Stations were selected if
they are located within the area of interest and have geodetic-quality location
and elevation information. As mentioned above, not all stations have geodetic-
quality location information or geodetic-quality height information, so not all can
be used for this purpose. The set of control stations was reduced further to
exclude those mounted atop manmade objects (e.g., an antenna, lighthouse,
range light, dock, bridge etc.) or those not mounted flush with the ground
surface. Geodetic control stations are preferentially situated near engineered
works (e.g., a railroad, highway, or commercial waterway) or atop accessible
high points (pers. obs. ; Kumler, 1994). Consequently, the set of station locations
is not representative of the full range of topographic conditions in the region. I
added the set of GPS-measured paleoshoreline data to the pool of check points so
that locations distant from engineered works can also be assessed.
Paleoshoreline data are suitable for this purpose because they contain sub-meter

location errors, typically contain sub-meter errors in elevation, and are, therefore,

150

of a higher-order than DEM data. Like control stations, paleoshoreline positions
were also preferentially selected and so, for example, do not include hill tops or
river valleys, but their inclusion adds important landscape variation that is
missing from the set of geodetic control station locations. Moreover, adding
paleoshoreline positions to the pool enables me to ensure that agreement exists
between the surface elevations I observed in the field and the surface elevations
stored in the DEM (see Chapter 5). A pool of 529 check points (256 NGS control
stations, 4 GDC control stations and 269 paleoshoreline positions) was used to
quantitatively assess DEM elevations.

A comparison of frequency histograms reveals that the distribution of
check point elevations (Figure 4.5a) is shaped and skewed like the distribution of
DEM elevations (Figure 4.5b) and suggests that the sample of check point
elevations is representative of the larger sample held by the DEM surface. The
check point distribution lacks, however, large spikes in the lowest elevation bins
because the elevations of open water bodies, which are represented in the

surface, are not represented in check point data.

151

80 200

   

29?
”E 60 o 150
V O
>, V—
0 v
5 40 5‘ 100
3 C
0' (D
e 3
u— 20 E 50
LL
0 0
200 300 400 500 200 300 400 500
Elevation (m) Elevation (m)
(a) (b)

Figure 4.5: Histograms of: a) 529 check point elevations; and b) all DEM
elevations in the study area. The difference between frequency scales is the
results of unequal sample sizes.

Select results of the first exploratory analysis

Ultimately, I conducted two exploratory data analyses of error. The first
led me to find a latent horizontal shift in the original NED- a systematic shift that
propagated through geoprocessing unnoticed and perturbed my attempts to
assess the distribution of error. Rather than report complete sets of results for
both analyses, however, I use this section to highlight interesting characteristics
of the original DEM that betrayed evidence of the shift. I use the next section to
report a complete accuracy assessment of the corrected and properly-situated
DEM.

Original DEM elevations were assigned to control point locations using

nearest-neighbor interpolation and GIS software. A scatterplot (Figure 4.6a)

152

suggested DEM elevations generally agreed with actual elevations. Results of a
Kendall’s test for statistical association (a = 0.10: coefficient = 0.897, p < 0.0000)

indicated a strong and significant correlation existed between the two sets.

 

450 5 450
g 400- g 400 5
C C
.9 .Q
5 ‘ 5 .
7;, 3001 E 300;
E 250; E 250;
o 5 o .
200* 200?
200 300 400 200 300 400
Actual elevation (m) Actual elevation (m)
(a) Original DEM (b) Corrected DEM

Figure 4.6: Scatterplots of DEM-reported and actual elevations of the (a) original
DEM and for (b) the corrected DEM.

I estimated errors in DEM elevations by subtracting check point elevations
from interpolated DEM elevations and then calculated summary statistics to
describe the distribution. Table 4.5 contains the first and second sets of summary
statistics. For example, the original sample mean difference (3? = -0.55 m) was

significantly different than zero at the 90% confidence level.

153

Table 4.5: Summary statistics that describe differences between actual and co-
located elevations in the original and corrected DEM surfaces.

The original DEM The corrected DEM

 

n 529 529

minimum -26.2 m -18.6 m

median -0.30 m ~0.02 m

mean (bias) -0.55 m -0.36 m

standard error of mean 0.27 m 0.18 m
standard deviation 6.79 m 4.07 m
maximum 27.8 m 19.8 m

Ultimately, I investigated possible covariates with error and was surprised
to find significant associations with the linear components of slope aspect.4
Circular measures of aspect {0 S aspect < 360 degrees} were decomposed into the
linear U (east-west) and V (north-south) components of a unit vector {-1, ,1} to
facilitate linear statistical analysis. A pure south-facing slope, for example, has a
V component value of -1, and a pure north-facing slope has a V component of +1.
Scatterplots (Figure 4.7) and results of Kendall’s tests for association both
suggested error was positively and significantly correlated with the east-west
component (tau = 0.199 and p < 0.0000), and negatively and significantly

correlated with the north-south component (tau = -0.287 and p < 0.0000).

 

4 I derived a surface of slope aspects from the grid of DEM elevations and assigned co-

located values to control points using GIS software.

154

Error (m)

 

-1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0

   

Aspect (u component) Aspect (v component)
(a) original DEM (b) original DEM
30 30
20 . 20
E ° ‘2
Lu -10 UJ
-20 —20
—30 -30
—1.0 —0.5 0.0 0.5 1.0 —1.0 —0.5 0.0 0.5 1.0
Aspect (u component) Aspect (v component)
(c) corrected DEM (d) corrected DEM

Figure 4.7: Scatterplots of DEM error and the linear components of slope aspect.

Although the statistical relationships were weak, the graphical evidence was
striking (Figure 4.7a and 4.7b) and indicated elevations in the original DEM

tended to overestimate elevations at locations with east- or south-facing slopes,

155

and underestimate elevations at locations with west- or north-facing slopes.
Such results indicated clearly that the DEM was not georeferenced prOperly.

I visually inspected control point and DEM data simultaneously using GIS
software and observed the apparent shift for the first time. Multiple attempts to
estimate the correct locations of control points within the footprints of nearby
grid cells yielded consistent estimates. On average, elevations in the original
DEM were shifted 75 m south and 15 m east of control point locations. So, I
corrected the DEM by translating the origin of the original NED surface 75 m
north and 15 m west, and reprocessed the model according to the methods
described above. Hereafter, any mention of ”the DEM” employed in this work
refer to the correctly georeferenced elevation surface.

Corrected DEM elevations were assigned to control point locations using
nearest-neighbor interpolation and GIS software and I conducted a second
exploratory analysis that yielded markedly improved results. For example, the
association between error and slope-aspect is now considered random,
uncorrelated and not indicative of any systematic bias (see Figure 4.7c and 4.7d).
The association between DEM-reported and actual elevation is stronger (see
Figure 4.6b) and suggests a better match (a = 0.10: Pearson’s correlation
coefficient = 0.9978, p < 0.0000), the sample mean and median values moved
toward zero, the two extreme error values have much lesser magnitudes, and the
sample variance diminished (see Table 4.5). These new results indicate that the

DEM is georeferenced more accurately than before.

156

Complete results of the second exploratory analysis

Again, corrected DEM elevations were assigned to control point locations
using nearest-neighbor interpolation and GIS software. Errors in elevation were
estimated by subtracting check point elevations from interpolated elevations. A
map of data postings (Figure 4.8) reveals no conspicuous trend or drift. Yet,
many small errors occur near other small errors, many positive errors are
situated near other positive errors and large negative errors tend to occur near
other large negative errors (although, in some instances, large positive errors are
situated near large negative errors). In short, differences from the sample mean
(-0.36 m) seem to exhibit spatial continuity or structure. Table 4.6 contains
statistical summaries of error, Figure 4.9 shows frequency histograms and Figure
4.10 shows q-q plots for the entire DEM and each subset. The calculated mean of
all DEM errors ()7 = -0.36 m) is significantly different than zero at the 90%
confidence level. Summary statistics and the frequency histogram (Figure 4.9a)
suggest the distribution of error is bell-shaped, symmetric and centered near
zero. The q-q plot (Figure 4.10a) reveals, however, larger-than-expected errors in
both tails. Results of a Shapiro-Wilk test for normality (a = 0.10: W = 0.917 and p
< 0.0000) indicate the standardized distribution of error is generally correlated

with, but does not significantly fit a Normal distribution.

157

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+ ‘ 4 . 1:. a
450 1 1. . .. ‘
O Q . l . 3 .
500 550 600 650 700 750
Easting (km)

Figure 4.8: Map of DEM errors at control point locations. The map reveals no
global pattern but suggests error values exhibit some spatial continuity at short
distances. The image is presented in color.

Elevations in the Lower Peninsula subset were collected originally from
contour lines either digitized or scanned from topographic maps. The Lower
Peninsula sample mean of calculated errors (f = -0.06 m) is not significantly

different than zero at the 90% confidence level.

158

Table 4.6: Summary statistics that describe differences between actual and co-

 

 

 

 

located DEM elevations.
The entire DEM Value Test for mean 95 0 Value
n 529
minimum -18.6 m
median -0.02 m
mean (bias) -0.36 m matched-pairs t p = 0.043
standard error of mean 0.18 m
standard deviation 4.07 m
maximum 19.8 m
Lower Peninsula subset
n 348
minimum -13.3 m
median 0.05 m
mean (bias) -0.06 m matched-pairs t p = 0.718
standard error of mean 0.16 m
standard deviation 2.94 m
maximum 13.1 m
Upper Peninsula subset
n 108
minimum -13.6 m
median -0.30 m
mean (bias) -0.50 m matched-pairs t p = 0.147
standard error of mean 0.34 m
standard deviation 3.57 m
maximum 7.0 m
Ontario subset
n 73
minimum -18.6 m
median -2.07 m
mean (bias) -1.58 m matched-pairs t p = 0.081
standard error of mean 0.90 m
standard deviation 7.65 m
maximum 19.8 m

 

159

 

150 150
E E
>. >
g 100 1 g 100
a: a)
D D
a a
u“. 50 E 50
0 O
-20 -10 O 10 20 -20 -10 0 10 20
Error (m) Error (m)
(a) entire DEM (b) Lower Peninsula subset
150 150
E E
5 6
C 100 . C 100
0: c0
3 D
8 8
u: 50 I: 50
0 :41: ".‘l 0 .....
-20 -10 0 10 20 -20 -10 0 10 20
Error (m) Error (m)
(c) Upper Peninsula subset ((1) Ontario subset

Figure 4.9: Histograms of elevation errors in the DEM.

Summary statistics and a frequency histogram (Figure 4.9b) suggest the
distribution of error is bell-shaped, symmetric and centered near zero, but may

contain larger-than-expected positive errors.

160

 

Sample quantiles
O

 

Sample quantiles
O

 

-2 -2
a"
_4 .. ~‘,_ -4
-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3
Theoretical quantiles Theoretical quantiles
(a) the entire DEM (b) Lower Peninsula subset
3
2 ,
g 0 ' g 1
3 r 3
o- , o- _
2 ’1 :2 0
a ' a.
E —2 -- E
“3 - m —1 :
(I) a) .
-3 '
-2
-2 -1 0 1 2 -2 -1 0 1 2
Theoretical quantiles Theoretical quantiles
(c) Upper Peninsula subset (d) Ontario subset

Figure 4.10: Q-Q plots of standardized elevation errors in the DEM.

The Lower Peninsula q-q plot (Figure 4.10b) reveals, however, larger-than-
expected errors in both tails. Results of a Shapiro-Wilk test for normality (a =
0.10: W = 0.930 and p < 0.0000) indicate the distribution or error in the Lower

Peninsula does not fit a Normal distribution.

161

Elevations in the Upper Peninsula were collected primarily using
photogrammetric techniques. Bolstad and Stowe (1994) compared
photogrammetrically-derived elevations at 42 NGS bench marks near
Blacksburg, VA and reported such values tend to underestimate actual
elevations. The sample mean of calculated errors ()7 = -0.50 m) for the Upper
Peninsula subset is less than zero and so suggests this model also tends to
underestimate actual elevations, but the sample mean is not significantly
different than zero at the 90% confidence level. A histogram (Figure 4.9c)
suggests the distribution of error is bell-shaped, but has large errors in the lower
tail. A q-q plot (Figure 9.10c) indicates the lower half of the distribution is not
well-behaved for it contains several values that are larger than expected should
errors be distributed as Normal. Results of a Shapiro-Wilk test for normality (a =
0.10: W = 0.930 and p < 0.0000) indicate the distribution of error in the Upper
Peninsula does not fit a Normal distribution.

Elevations in Ontario, Canada were likely derived from the DTED and
coerced into the NED. Summary statistics and a frequency histogram (Figure
4.9d) suggest the distribution of DEM error is skewed left and centered below
zero. The Ontario subset contains extreme values and they are the same as those
associated with the entire DEM. The sample mean of calculated errors (J—C = -1.58
m) is significantly different than zero at the 90% confidence level and the sample
standard deviation (7.65 m) is relatively large. As expected, elevation data for

Ontario contain large errors and so should be considered a likely source of

162

uncertainty in model results. A q-q plot (Figure 4.10d) suggests that the
distribution of error might not be distributed as normal, but results of a Shapiro-
Wilk test for normality (a = 0.10: W = 0.982 and p = 0.364) indicate the
distribution or error does fit a Normal distribution.

I partitioned the DEM into three subsets based on ancillary information
about the original DEM production methods. I expected to find marked
differences in the resultant behaviors of their elevations and errors. It seems,
however, that subsequent geoprocessing mitigated (or obfuscated!) many of the
apparent differences, for only the Ontario subset appears stands out with its
relatively large mean and variance. 1 transformed this observation into a
hypothesis and conducted three, two-sample difference-of—means tests to assess
statistical differences (a = 0.1, m = 0.0 m and assuming unequal variances). All
test results (Table 4.7) indicate, however, that no statistical difference exists
between the means. Nevertheless, I continued to work with the three subsets

because each contains data derived from different source materials.

Table 4.7 : Results of two-sample difference-of-means tests among DEM subsets.

Lower Peninsula Upper Peninsula
Upper t =1.164
Peninsula df = 107
p value = 0.233

 

Ontario t = 1.612 t =1.126
df = 72 df = 72
p value = 0.201 p value = 0.274

 

163

Covariations with location, elevation, and slope

Bolstad and Stowe (1994) reported large discrepancies between ground-
based and DEM-reported elevations tend to occur along steep slopes and ”in
high-relief forested areas” (p1329), thus implying DEM errors exhibit spatial
continuity and covary with other landscape elements. Such ideas about spatial
continuity are not unique for others also have reported spatial patterns of error
(e.g., Holmes et al., 2002, Kyriakidis et al., 1999; Hunter and Goodchild, 1997; and
Veregin, 1997), but they are important because they provide grist for examining
error in terms of location, elevation and other landscape attributes. Specifically,
Bolstad and Stowe (1994) claim dense tree canopies negatively impact the
precision of some DEM production methods, and photogrammetric image
correlations can fail in areas with steep slopes. Such imprecision and failures
yield inaccurate data for those locations. From this information, I plotted maps
(not shown), reviewed field notes and examined datasheets for check points
associated with large errors (> | 8 ml). Indeed, I found many that occur in high-
relief or forested areas (NGS datasheets contain descriptions of the approach and
area near control stations). Station R]1215 (error = -13.6 m) is situated atop a
high and forested knoll, station R]1118 (error = -12.0 m) is mounted along a large
outcrop of limestone, and station R]0383 (error = -13.6 m) is situated near the
peak of a high and steep hill of sand. Station PL0631 (error = -8.8 m), however, is

situated on flat and open ground.

164

Of the thirty-four control points that have large absolute errors, only four
are NGS control stations; the others are paleoshoreline sites. Had I not already
assessed the quality of my paleoshoreline data (mean = 0.16 m, standard
deviation = 0.77 m), then I might have considered this result to be an indictment
of the lesser quality of my paleoshoreline data. Instead, I believe that many of
the large errors (> I 8 ml) are associated with ground slope and data model
imprecision. Elevations in the DEM grid are spaced at 45-meter intervals that
span terrain discontinuities and cannot capture finer-scale variations in
topography (Maune, 1996; Carter, 1992; Shearer, 1990). Many relict lake bluffs,
for example, have steep slopes that rise from toe to top over runs less than 45
meters - all within the footprint of a single grid cell. Consequently, the DEM
will, by design, contain errors that covary with such breaks or changes in slope.

Check-points have location, elevation and error attributes so relationships
among these variables can be assessed easily. To assess the relationship between
error and slope, however, I derived surfaces of slope gradients and slope aspects
from the grid of DEM elevations and assign co-located values to control points
using nearest-neighbor interpolation and GIS software. Any comparison
between an elevation error and an elevation-based derivative, like slope gradient
or aspect, presupposes extant errors in elevation do not influence the slope
values derived for the same locations. Such a presupposition is unreasonable,

especially since Carter (1992) demonstrated how gradient and aspect calculations

165

are sensitive to even small elevation errors, but I continued for the sake of

exploration.

Table 4.8: Results of Kendall’s tests for association between easy-to-measure
landscape variables and: a) signed error and b) unsigned error.

a) signed error b) unsigned error

 

 

 

 

The entire DEM tau p value tau p value
Easting 0.021 0.476 0.126 < 0.001
Northing -0.037 0.204 0.178 < 0.001
Elevation -0.053 0.067 0.074 0.011
Slope gradient 0.033 0.256 0.273 < 0.001
Slope aspect (U) 0.004 0.902 -0.007 0.804
Slope aspect (V) 0.051 0.078 0.035 0.227

Lower Peninsula subset
Easting 0.108 0.003 0.018 0.621
Northing -0.003 0.928 0.085 0.018
Elevation -0.062 0.083 0.021 0.563
Slope gradient 0.039 0.275 0.308 < 0.001
Slope aspect (U) 0.024 0.498 0.019 0.598
Slope aspect (V) 0.140 < 0.001 0.050 0.160

Upper Peninsula subset
Easting 0.050 0.444 -0.032 0.619
Northing 0.021 0.750 -0.034 0.604
Elevation -0.062 0.344 0.176 0.007
Slope gradient 0.076 0.244 0.331 < 0.001
Slope aspect (U) 0.043 0.512 -0.017 0.799
Slope aspect (V) -0.145 0.026 0.099 0.128

Ontario subset

Easting -0.424 < 0.001 0.174 0.029
N orthing 0.287 < 0.001 -0.207 0.010
Elevation -0.006 0.943 -0.046 0.567
Slope gradient -0.168 0.036 0.051 0.520
Slope aspect (U) 0144 0.071 0.034 0.675
Slope aspect (V) -0.003 0.970 0.057 0.478

 

166

I used scatterplots (not shown) and Kendall’s non-parametric test for association
to examine the relationships between error and location, elevation and slope. I
examined unsigned errors as well. Table 4.8 lists the results. A strong association
between variables is indicated when there is a large probability that the ranks of
data are in the same order (tau > 0.667). Of all the relationships tested, none
exhibited a strong association. Jumbled pairings (tau < 0.333) or statistically
insignificant test results (p > 0.100) eliminate the need to consider most of these
relationships further. A few, however, exhibit moderate (0.333 < tau < 0.667) and
significant (p < 0.100) associations, so I focused on them.

Unsigned error is positively correlated with slope gradient in every set,
although results for the Ontario subset are weak and not statistically significant.
These results are reasonable because they suggest large errors occur in locations
where elevation is hard to measure -- along steep slopes -- and they agree with
results reported by Bolstad and Stowe (1994) and Hunter and Goodchild (1997).
A scatterplot of this relationship offers conflicting evidence (Figure 4.11)
however, for it shows the full range of error occurs at locations with relatively
shallow slopes (< 5% gradient). Also, both point clouds show no linear patterns
of association.

The relationship between error and slope gradient provides grist for
general conclusions only. Carter’s (1992) work cautions that gradient
calculations are uncertain given errors in the elevation model. From these

results, steep slopes can be associated with large DEM errors, but both large and

167

small DEM errors can occur along any slope regardless of gradient. Therefore,
an error estimate cannot be reduced if the terrain is known to have a low
gradient.

The only other moderate correlation among error and location is in the
Ontario subset and it indicates error decreases in an easterly direction. Review
of ground control data, however, provides a reason for why this test result might
not be a valid result. Ground control data used to assess the Ontario portion of
the DEM are highly clustered (Figure 4.12a). They contain only four GDC
control stations - the balance are paleoshoreline positions collected at field sites.
Paleoshoreline data near Sault Ste Marie, Ontario, for example, were collected by
Cowan (1985) and his data comprise the northwestern cluster. Figure 4.12b
reveals most DEM elevations tend to overestimate elevations in this cluster.
Paleoshoreline data at St. Joseph Island were collected by Karrow (1987) and his
data comprise the central cluster. DEM elevations tend to overestimate Karrow’s
elevations, but not always. And, I collected paleoshoreline data at Cockburn
Island, which comprise most of the southeastern cluster. DEM elevations tend to
underestimate elevations in this cluster, but not always. In short, the test for
association between error and Easting is seemingly influenced by the
interrelations among three distant clusters and not among seventy-three well-
distributed observations (Figure 4.12b). Consequently, the test statistic has likely
been overestimated and the associated p value is too small. I did not to pursue

this association further.

168

20 “1'- 20

   

E
a) 15 g

A 'D l

E g 9'7

.5 g, 10

t m

m E
‘9' 5
LE

-20 0
0 5 10 15 20 0 5 10 15 20
Gradient (percent) Gradient (percent)
(a) (b)

Figure 4.11: Scatterplots of: a) signed error and slope gradient; and b) unsigned
error and slope gradient. Black lines drawn to emphasize zero error.

 

 

20
660 -
:E: . . 7.1.. ‘_ , A 10 .
C ‘, h " . .
11.. 1 1 ,
t 620 -. ~_." - - a Li , l, 1112*» g
o 1 1 . 4:. '1‘ . .7 at.
Z . _. " - -. . -1o ‘
1 -' @4155. - "‘1‘ ‘ ,1 -=‘.‘x,,, : . > 1 j, . ~1~ ' {r 1, fi
—20
620 640 660 680 700 620 640 660 680 700
Easting (km) Easting (km)
(a) (b)

Figure 4.12: Map and scatterplot of ground control locations used to assess error
in the Ontario subset.

169

Spatial autocorrelation

The distribution of DEM error (Figure 4.8) seems to exhibit some form of
local spatial continuity or structure - meaning two errors located close to each
other tend to have more similar values than two errors that are far apart (after
Isaaks and Srivastava (1989:50—51). This is structure that cannot be explained by
the weak associations with location, elevation or slope. The semi-variogram is a
useful tool for exploring and characterizing the way in which the deviations from
a mean value at different locations covary or are correlated (Bailey and Gatrell,
1995: 162). Yet successful use and interpretation of a semi-variogram of errors
presupposes an understanding of regionalized variables and the assumptions of
stationarity. These concepts are much more closely aligned with the spatial
models discussed in Chapter 5 than with the accuracy assessments presented

here, so I report these results in Chapter 5.

Summary

I designed my sampling and data processing protocols (Chapter 3, this
volume) to ensure that paleoshorelines were measured as accurately as possible
given the lesser precision of GPS technology relative to traditional yet more
labor-intensive technologies. Careful planning and diligent use has yielded a set
of measured positions that closely match actual positions. Measurement errors
in elevation are random, typically sub-meter and always less than two meters;

the distribution is centered near zero and Normal. Horizontal errors are

170

negligible. There is no evidence of any remaining gross or systematic error that
can or should be mitigated.

Selection errors in paleoshoreline data present a problem because they
cannot be easily identified or redressed. Gravel lags are the best indicators of
former shorelines, but using them as indicators of shoreline elevation is
imprecise. I suspect such errors are often ignored during spatial modeling and
analysis. In this case, however, the range of possible selection errors is large
enough to exceed the three—meter critical threshold I adopted for distinguishing
different water levels, and so they warrant further consideration. A position
with a three-meter selection error is not acceptable for use, but I do not know if
any of my data contain such an error. Consequently, my only recourse is to add
the information I do have about possible selection errors to my spatial model. In
short, I need to simulate their existence in order to ascertain how they might
impact my results.

The US Coast Guard archive of GPS Status Message Reports (US Coast
Guard Navigation Center, 2004) is a valuable resource; I did not know it existed
until after I collected data and began analysis. The US Coast Guard posts status
reports that list planned outages and system changes as well as recent and
unexpected satellite behaviors (such as the one I encountered). This kind of
information will impose additional constraints on future planning missions, but

it will add value to any data I collect with GPS in the future.

171

The NED is the best available source of ground surface elevation data for
the region of interest. Unfortunately, these data contain both large and small
errors that are the results of a long and complex geoprocessing history. Analysis
of the NED has provided the biggest surprise for I did not expect to find a
systematic bias in location. I translated the NED surface 75 m north and 15 m
west and, subsequently, removed a systematic pattern of elevation errors and
reduced the sample mean, median and variance of errors. Simultaneous
visualization of the corrected surface and check point data provides solid
evidence of a better fit. I have since revisited all NED-related documents on the
USGS website and scoured the literature for any report that might address the
shift I observed, but I have found no report that does so. I forwarded my results
to the USGS, but have not yet received a reply.

Although corrected, the DEM still holds a pool of variations associated
with topography, artifacts of DEM production methods, and adulterations
imposed by various geoprocessing algorithms. Partitioning the model into three
subsets has proven useful for it has allowed me to isolate some of these
variations and consider their impacts. The distribution of elevations in the
Ontario subset, for example, is clearly dominated by artifacts of a data
production process. Had I not subset the model, the non-topographic pattern of
spikes in the Ontario histogram would have remained largely hidden in the
histogram of DEM elevations. Elevations in the Lower and Upper Peninsula

subsets also exhibit artifacts of data production processes, but these appear mild

172

by comparison. By and large, the Lower and Upper Peninsula subsets contain
elevations that represent surface topography.

Mapped errors in DEM elevations exhibit evidence of local spatial
continuity as positive errors tend to occur near other positive errors and negative
errors tend to occur near other negative errors. Yet, correlation test results
demonstrate DEM error, either signed or unsigned, does not covary with location
coordinates, elevation, or slope. Moreover, trend surface analyses (not reported)
provided no statistical power to suggest otherwise. The apparent association
between unsigned error and slope gradient is acknowledged but the parameters
that might define its behavior are uncertain because gradient calculations are so
sensitive to errors in elevation (Carter, 1992) and the DEM employed in this work
certainly contains errors in elevation. In my opinion, no correlation is
sufficiently strong to advocate using knowledge about it to improve estimates of
error at unsampled locations. While it would be convenient to have found a
strong and significant association between error and location, elevation, or slope
- or any other cheap-to—measure landscape variable for that matter - other means
of qualifying spatial continuity are necessary. I take up this issue again in
Chapter 5.

Absolute errors in DEM elevations often exceed three meters and, in
Ontario, can reach almost twenty meters. Such errors far exceed the critical
threshold I’ve adopted for distinguishing different water levels. The DEM, as is,

is not fit for my use. Unfortunately, the current DEM is the best one available,

173

and so I must use it. My only recourse is to add the information I do have about
DEM errors to my spatial model. In short, I need to fix the elevations errors
where I know they occur, and I need to simulate the presence of error at locations
between check point locations. Doing so will enable me to ascertain how they

might impact my results.

174

CHAPTER 5: THE SPATIAL MODEL

Introduction

This chapter describes a spatial model for digitally reconstructing ancient
landscapes associated with glacial Lake Algonquin. The model has two parts.
The first part reconstructs water planes that have been upwarped by differential
isostatic rebound over the past 11,000 years. Initial reconstructions are
supported by paleoshoreline data (described in Chapter 3) and parameters that
describe the upwarped surface are estimated via least squares. Water planes are
reconstructed ultimately via universal kriging, which yields both a prediction
surface and an estimate of uncertainty at each predicted location. The second
part of the spatial model addresses error and uncertainty about error in a
contemporary digital elevation model (DEM), which is used to represent ground
surface form for the region of interest. A set of control points and information
about elevation errors at control point locations is used to condition the DEM
and, via ordinary kriging and Monte Carlo simulation techniques, to generate
alternate possible realizations of the ground surface. Finally, results of the two
parts (a predicted water plane and a set of alternate possible DEMs) are
combined to allow locations within the area of interest to be characterized as:
above water plane; below water plane; or uncertain. Four landscapes are
reconstructed and they are associated with the Main, Ardtrea, Upper Orillia, and

Lower Orillia phases of glacial Lake Algonquin.

175

I offer a review of geostatistical concepts that underlie general spatial
prediction and kriging before presenting the spatial model and its two parts. My
review summarizes essential points related to the theory of spatial prediction,
but does so in a user-friendly format. Formal treatments of these theories and
methods are presented by Journel and Huijbregts (1978), Isaaks and Srivastava

(1989), Bailey and Gatrell (1995) and Gringarten and Deutsch (2001).

Modeling outcomes of a spatial random process

A field is a conceptual model that is useful for representing an attribute of
a phenomenon that varies over space. Elevation, for example, is an attribute of
terrain and it varies over space. Similarly, relative humidity and air temperature
are attributes of the atmosphere that vary over space. A field model typically
represents space by employing a tessellation of discrete spatial elements (e.g.,
points, grid cells, facets etc.) that are assigned values taken from the
phenomenon of interest. This work utilizes a two-dimensional tessellation of
discrete grid cells. Field models are always approximate because ”we cannot
store an infinite number of locations” (Cova and Goodchild, 2002:511) and we
cannot collect or store attributes with infinite precision.

Any procedure or process used to take measurements of a phenomenon
has finite precision, so data obtained from measurements are imperfect. The
difference between a measured value and the actual value is error. The amount

of error in any measured value is always unknown, however, because the true

176

value exists beyond the limits of equipment or procedural precisions. Because of
this inescapable error, the amount of error in a measured value is considered a
random variable. An elevation value obtained from measurement is also
considered a random variable because it contains a component of fixed truth and
a component of random error. A process that generates a random variable is a
random process. Accordingly, a process for measuring elevations at locations
over a region of interest is considered a spatial random process.

Other spatial processes can influence the outcomes of a spatial random
process. Consider, for example, an instance of terrain that is flat, easy to access
during calm weather and, so, relatively easy to measure given equipment
provided (i.e., conditions for taking measurements are optimal). An elevation
value taken under such conditions might be expected to contain random error
associated only with variation that occurs beyond the limits of equipment or
procedural precision. Alternatively, consider an instance of terrain that is rough,
difficult to access during stormy weather and, so, very difficult to measure given
the equipment provided (i.e., conditions are not optimal). An elevation value
taken under such conditions might be expected to contain an error greater than
that generated by equipment precision alone because external forces upset the
measurement process. Using these two instances as ”straw men,” it is easy to
imagine spatial gradients of terrain (from flat to rough) and weather (from calm
to stormy) and how they might interact across space and time and, so,

differentially perturb the measurement process from one location and one

177

moment to a next. Consequently, a random measurement process can generate a
field of random variables that contain noisy errors associated with equipment
precision as well as spatial patterns of error introduced by external phenomena
that differentially upset the process. Unfortunately, we do not always know
where or when a spatial error process (or processes) exists or how such a process
might alter our best efforts to collect data in the field or lab.

A random field is a conceptual model that is useful for representing the
outcomes of a random spatial process. 1 Use of a random field assumes variation
over space can be expressed as the sum of three components: a deterministic
component akin to either a constant mean or spatial trend (J ournel and
Huijbregts, 1978: p40, prefer the term ”drift”); a random and spatially structured
error component; and a random but spatially unstructured error component (i.e.,
noise). In short, the outcome at each location is considered a random variable,
the set of all random variables across the region of interest comprises a random

field, and a specific set of measured outcomes within the region of interest is

 

1 Many geostatisticians use the phrases regionalized variable (Journel and Huijbregts,
1978; Burrough, 1991) or random function (see Kyriakidis et al., 1999; Goovaerts ,1997; or
Issaks and Srivastava, 1989), but I prefer to use the phrase random field (see Diggle and
Ribeiro Jr, 2002; or Ehlschlaeger, 2002) because it provides an explicit link to the field
data model (Couclelis, 1992; Cova and Goodchild, 2002), and doing so averts confusion

with other uses of the term function.

178

considered a realization of that random field. Following Burrough (1991), a

random field is expressed as:

Z(u) = m(u) + e’(u) + e”, Vu E R [Eq. 1]

where Z(u) is the random field, m(u) is either the constant mean or spatial trend
component, e’(u) is the random and spatially structured error component, 8” is
the random and spatially unstructured error component, and u is the set of all
locations in the region of interest R. Let u..-, i = 1,. . .,n, represent a set of 11
locations where the random field Z(u) has been observed in region R, and let uo
represent unsampled locations in region R.

The probability density function (pdf) of a random field Z(u) is a model of

possible values that 2 can take at locations u and their associated probabilities:

f(u; z) = Prob { Z(u) = z }, V 2 [Eq. 2]

Because the probability at a single point in a continuous distribution is always
zero, a pdf is, for practical purposes, often expressed in terms of the integral
between two points in the distribution.

The cumulative distribution function (cdf) is a model that defines the

probability that outcomes of Z(u) do not exceed a given threshold 2 :

F(u; z) = Prob { Z(u) S 2 }, V 2 [Eq. 3]

179

If additional information exists and can be used to condition the random field,
then the conditional cumulative distribution function (ccdf) of the random field
Z(u) defines the probability that outcomes do not exceed threshold 2 given this

information:

F(u; z | (info)) = Prob { Z(u) S 2 | (info) }, V 2 [Eq. 4]

The expected value or spatial trend m(u) and spatially unstructured error
8” components are models covered in many statistical texts, so another review
here would be redundant. I focus instead on the basis geostatistics provides for
exploring and modeling the random and spatially structured component £’(u).
Spatial structure implies a relationship between proximity and similarity of
outcomes: two outcomes located close to each other will tend to have values
more similar than two outcomes that are farther apart (after Isaaks and
Srivastava, 1989). According to Bailey and Gatrell (1995), if we expect a random
field to exhibit spatial structure, then we can anticipate ”observing positive
covariance or correlation at short distances and lower covariance or correlation at
greater distances” (p 162). Covariance C() is a measure of similarity between

outcomes u.- and u; and can be expressed as:

C(ui, “1) = El (Z(ui) - m(w» ' (Z(Ui) - m(ul» } [1361- 5]

180

Modeling the spatial component of a random field often requires
adopting one or more assumptions when complete knowledge is not available
for all locations within the region of interest. For example, it is not always
possible to estimate the cdf at a given location because, typically, at most only
one observation is available at that location (Shortridge, 2001). So, we must
adopt assumptions about the cdf if we want to proceed with sparse data. The
assumption of stationarity, for example, holds the expected value and variance of
the random field Z(u) are independent of location, or m(u) = m and 02(u) = 02.
Adopting this assumption allows the cdf at any location to be characterized by
the cdf of the random field. A more commonly used but weaker assumption is
intrinsic stationarity, which assumes a constant mean and a constant variance in
”the differences between values at locations separated by a given distance and

direction” (Bailey and Gatrell, 1995:162). In geostatistical notation:

E [Z(u) - Z(u + h)] = 0 [Eq. 6]

Var [Z(u) — Z(u + h)] = E 1 [Z(u) — Z(u + 1012} [Eq. 71

where h is a vector of distances (or distances and directions) that separate pairs
of outcomes. Adopting the weaker assumption removes focus from the absolute
locations of data and estimating joint cdfs that are supported by few observations
and, rather, places focus on the more-numerous distance vectors that separate

pairs of random variables. In this sense, spatial structure implies two outcomes

181

located close to each other will tend to have more similar values than two
outcomes far apart (after Isaaks and Srivastava (1989:50-51) - regardless of absolute
locations. Covariance between outcomes (Eq. 5) can be re-characterized in terms

of separating distances:

C(11)= E {Z(U) ' Z(u + h)} - E{Z(U)} '1“3{Z(u + h)} [Eq- 8]

or, by assuming intrinsic stationarity and substituting a constant mean, m, as:

C(h) = E [Z(u) — Z(u + h)] — m2 [Eq. 9]

Note, stationarity and intrinsic stationarity are not properties of any
phenomenon, but modeling decisions that provide reasonable means of
analyzing a random field given sparse data or scant information about data.

A variogram 2y(h) is the expected squared difference between data values
separated by vector h (Gringarten and Deutsch, 2001). A variogram can be

expressed as:

2101) = Var 12(10— Z(u + h)] = E 1 [Z(u) - Z(u + h)] 21 [Eq. 101

The semi-variogram y(h) is one-half the variogram 2y(h) and a measure of

variability used commonly to explore spatial structure in data. Semi-variance

182

values increase as outcomes become dissimilar and tend towards zero as
outcomes become similar.

Again, covariance C() is a statistical measure of similarity and, under the
assumption of intrinsic stationarity, inversely related to semi-variance. By
definition, the covariance at h = 0, or C(O), is the variance 0?- (Gringarten and
Deutsch, 2001). Covariance C(h) is 0 when values separated by h are not
correlated. Combining these relations and the concepts embodied in Equations 9

and 10, the link between semi-variance and covariance is:

100 = C0) - C(h) or C(h) = 02-101) 024.111

The link between semi-variance and covariance provides the basis for
interpreting a semi-variogram. The ”sill" of a variogram represents the variance
02 of the random field and it corresponds with no spatial correlation. If Z(u) and
Z(u + h) are positively correlated, then corresponding semi-variance values are
less than the variance, or sill. If Z(u) and Z(u + h) are negatively correlated,
however, then corresponding semi-variance values are greater than the variance,
or sill. The ”range” of a semi-variogram is the distance h at which observed
semi-variance reaches the sill and spatial correlation no longer occurs. Also, a
”nugget” effect might be observed at very short distances. A nugget effect is
interpreted as random chaotic or nonlinear variations ” that have no spatial

autocorrelation structure” (Gringarten and Deutsch, 2001: 509)

183

For computation, the semi-variogram is expressed as:

n(h)

11h > = 2751—1 21201-1 z1u. +1012 1124121

where n(h) is the number of outcomes separated by each distance (or direction)
in vector h. Given sparse data, however, values of h typically represent lags or
small ranges of distances approximately equal to h (i.e., within some tolerance).
When used within a kriging framework, the theory of random fields and
spatial structure can be employed to predict outcomes at unsampled locations
(i.e., interpolation). According to Bailey and Gatrell (1995), if covariance exists
between observed outcomes, then outcomes at unsampled locations ”are not
entirely unpredictable" (p183). A kriging framework accomplishes spatial
prediction by modeling unsampled outcomes as weighted linear combinations of
sampled outcomes. In practice, kriging weights are assigned with respect to: a) a
model of covariances observed among sampled outcomes; and b) a model of
covariances expected between sampled and unsampled locations. Kriging
weights are subject to linear constraints that ensure the expected squared

prediction error is zero. In geostatistical notation, a set of kriging weights is:

401,0) = C‘1c1u.-,o) [Eq. 131

184

where Mum) is the set of weights; C —1 is the inverse of a matrix holding
covariances between sampled outcomes; and C(ui,0)is the set of expected
covariances between sampled and unsampled locations uo. In practice,

expected covariances C(h) between sampled and unsampled locations are

modeled as a function of distance between u0 and nearby u ,- . Given a sample,

distances between sampled and unsampled locations, and information about the
spatial structure of covariance over space, the set of predicted outcomes at

unsampled locations becomes:

11
Z(uo)=211u.~,o)Z(u.-) 1124141
i=1
A kriging framework can be used to model uncertainty at predicted locations.

The mean square prediction error (a.k.a. kriging variance, 0'3 ) is modeled by

removing the portion of variance explained by spatial structure from the total
variance 02. As the amount of variance explained by spatial structure
approaches zero, the kriging variance approaches the total variance 02. This link

can be expressed as:

at = 02 —cT1u.-,o)C‘1c1u.,o) [Eq. 151

185

or, by substituting kriging weights (Eq. 13) for C ‘1c(u,-,0) , as:

2 2 T
00 =0 'C (111,0)40110) [HQ-16]

An expected value Z(u,- )and a kriging variance 03 are sufficient for specifying a

cdf at each location (if we also assume the distribution of values at each location
is distributed as Normal). Furthermore, information provided by nearby
random variables allows a ccdf to be specified. Therefore, alternate possible
realizations can be generated at each location in the region of interest by drawing
values randomly from each ccdf.

Sequential Gaussian simulation (sGs) is a technique for generating
alternate realizations of a random field that can be used as inputs to a spatial

model. According to Goovaerts (1998:4),

”sequential simulation amounts to modelling the conditional
cumulative distribution function (ccdf), ,then sampling it at each
of the grid nodes visited along a random sequence. To ensure
reproduction of the z-variogram model, each ccdf is made
conditional not only to the original It data but also all values

simulated at previously visited locations.”

The promise of using not a single realization, but multiple alternate realizations

of a random field is the ability to reveal uncertainty in results of a spatial model

186

given uncertainty about errors in data. When used within a Monte Carlo
simulation framework, sequential Gaussian simulation can reveal uncertainty in
results accurately and precisely (Goovaerts, 1998).

Monte Carlo simulation is a computer-intensive framework that is useful
for revealing contributions of input data errors to results, differences among
uncertainties across a geographic region of interest (Burrough and McDonnell,
1998) and uncertainties that lurk in spatial model results. In essence, a typical
simulation consists of evaluating a spatial model many times, each time using
input data that have been modified randomly via a model that expresses an error
distribution or makes assumptions about error behavior. Parameters of the
model are derived with respect to known or assumed information about errors in
the input data. After a set of 11 input realizations is generated, the spatial model
is run 11 times and the set of n spatial model results is summarized to determine

the range of possible outcomes at each location.

Building the spatial model

Schaetzl et al. (2002) built a spatial model for interpolating paleoshorelines
along four glacial Lake Algonquin water planes; Figure 5.1 diagrams their
workflow. In essence, a differentially upwarped water plane was modeled as a
function of location using paleoshoreline position data and a second-order
polynomial surface model with parameters estimated via ordinary least squares.

The minimum measured paleoshoreline elevation value was subtracted from the

187

upwarped surface and the result represented differential warping relative to the

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Figure 5.1: The spatial model Schaetzl et al. (2002) used to reconstruct
landscapes in northern Michigan associated with glacial Lake Algonquin.

188

Next, the relative rebound surface was subtracted from a contemporary
digital elevation model (DEM), thereby generating a topographic surface that
was down-warped (i.e. differentially depressed) by the immense weight of the
Laurentide ice sheet; this is similar to the method used by Krist and Schaetzl
(2001). Finally, adjusted elevation values were classified with respect to the
aforementioned lowest feature; DEM cells with elevation values greater than the
lowest feature were classified above water and the balance was classified not above
water. The binary classification scheme served to cartographically flood the
depressed landscape, reveal the extent of the modeled water plane as constrained
by topography and, hence, interpolate paleoshorelines at locations between
measured paleoshoreline positions.

Others have built similar models for reconstructing ancient water planes
in Scotland (e. g., Smith, Cullingford and Firth, 2000; Firth, Smith and
Cullingford, 1993) and interpolating paleoshorelines in Canada (e. g., Leverington
and Teller, 2003; Leverington, Teller and Mann, 2002), but each assumed
paleoshoreline data do not contain measurement errors (Poole and O’Farrell,
1971), which in my experience is not always the case. Consequently, their results
are deterministic and do not convey any imprecision or uncertainty.

I use a model similar to the one built by Schaetzl et al. (2002), but instead
of generating a single deterministic result, I employ kriging methods and
sequential Gaussian simulation (sGs) Within a Monte Carlo framework to take

advantage of information I have about random errors in my paleoshoreline data

189

and digital elevation model, respectively. Figure 5.2 diagrams my workflow.
The enhanced spatial model allows me to identify locations in my results that are
subject to greater or lesser uncertainties. Knowing which locations suffer greater
uncertainties is useful for qualifying my results (and prescribing limited uses)
and for focusing subsequent fieldwork.

Below I present the two major parts of the paleoshoreline interpolation
model. The first part acknowledges possible errors that lurk in the
paleoshoreline dataset and limitations associated with using ordinary least
squares (OLS) to estimate upwarped water plane elevations. The second part
acknowledges errors that lurk in the DEM and describes the models I use to
generate alternate possible realizations of the contemporary ground surface.
Ultimately, the results of these two parts are combined so that a comparison can
be made at every DEM grid cell location between the elevation of the
contemporary land surface and the elevation of the differentially-upwarped
water plane. Unsampled locations with ground surface elevations equal to, or
very near to, the co-located water plane elevation are identified as candidates for

having unsampled paleoshorelines.

190

   

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 5.2: The spatial model used in this work to digitally reconstruct water
planes and landscapes in northern Michigan and western Ontario that were
associated with glacial Lake Algonquin. The model was run 100 times for each
water plane, which produced a set of 100 results that were summarized to reveal

the influences of input data errors.

191

Models of elevation errors in paleoshoreline elevation data
Errors in paleoshoreline elevation data are treated as the sum of random
and independent and selection errors and measurement errors. I use a statistical

model to express these errors and mitigate their influence.

Assumed model of selection errors

Uncertainty about selection errors in my paleoshoreline data can be
addressed by adopting assumptions about selection error and employing a
model based on those assumptions (Shortridge, 2001). Based on my experience
in the field and via an analysis of the research of others (e. g., Lawson, 1891 ;
Goldthwait, 1910; Morton and Speed, 1998), I expect most surveyed elevations
are accurate proxies for former water levels. I expect, however, that some
measured elevations might overestimate water levels because: a) the base of a
wave-cut bluff typically forms at or slightly above water level; b) the
bouldery/ gravelly lags that form at the bases of wave-cut bluffs vary in width
(pers. obs.) according to local wave conditions and water levels fluctuations
(Chapter 2); and c) I began my search for the bouldery/ gravelly lag at the highest
point along each base. Accordingly, my search method preferentially selects the
highest portion of each the bouldery/ gravelly lag. Therefore, there is a
possibility that the highest measurable point on a particular bouldery/ gravelly

lag might overestimate average water.

192

I assume most selection errors to be 0m because I expect most surveyed
features represent water levels. Wherever errors do occur, I assume most will be
small and fall within the interval of 0 and 1 m. I must recognize that, on rare
occasions, an extreme error might exist and I assume it will fall within the
interval of 1 and 3 m. I do not have reason to expect any selection error will
exceed three meters. Selection error at any paleoshoreline location can be
modeled as a random variable that is distributed as Exponential. I chose the
Exponential distribution for its convenience: it can be adapted easily to describe
the expectations and assumptions I have about selection errors (i.e., bounded by
zero and decreasing probabilities with increasing error values). The Exponential

probability density function is expressed as:

f(x)=%e—(x_#)/fl x2#;/5’>0 [liq-17]
where: x is a value in the distribution; )1 is the mode of the distribution; and [3 is
the mean of the distribution. The specific selection error model employed here
assumes an Exponential distribution with parameters )1 = 0.0 m and ,8 = 0.33 m.
— (x) / 0.33

f (x) = 3e [Eq. 18]

Selection errors are assumed to be spatially unstructured. A histogram (Figure

5.3a) shows one realization of 529 selection errors (one for each paleoshoreline

193

sample I have) that were generated using the Exponential model. Note the
distribution is bounded by a value of zero and the frequency of a particular

selection error occurring decreases with an increase in value.

Empirical model of measurement errors

Uncertainty in measurement error can be addressed by characterizing the
measurement process and employing a model based on the characterization
(Shortridge, 2001). In Chapter 3, I reported elevation errors measured at NGS
control stations. From my assessment of these values, measurement error is
modeled as a random variable that is distributed as Normal. The Normal

probability density function is characterized as:

e“(x‘#)2 /<2oz)
f(x)=
am

 

[Eq. 19]

where: x is a value in the distribution; u is the mean of the distribution; and o is
the standard deviation. The specific measurement error model (Eq. 20) assumes
a Normal distribution with parameters taken from the sample of control station

errors: u = 0.16 m and o = 0.77 m.

e—(x-0.16)2 /1.1858

f (x) = 1.9301 We 20]

 

194

A second histogram (Figure 5.3b) shows a realization of 529 measurement errors,
which is the same number of ground control points that I have available, that

were generated using the Normal model and parameters described above.

250 “i 250
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Selection error (m) Measurement error (m)
(a) (b)

Figure 5.3: Histograms of errors generated randomly. Error values are binned in
0.25 m intervals.

Model of cumulative errors

Paleoshoreline elevation data are subject to the limits of precision
associated with the method I used to select relict shorelines and the limits of
precision associated with the method I used to measure relict shorelines. I
assume selection errors are not spatially structured, since I have found no
evidence that suggests they are. Moreover, I assume each spatial error process

exists independently of the other, for I have no reason to believe they do not.

195

Therefore, the cumulative error in any paleoshoreline elevation can be modeled
as the sum of assumed selection and inferred measurement errors. The expected
value (i.e., mean) of the sum of two or more random variables is the sum of the
respective means. In this case, the expected selection error is 0.33 m and the
expected measurement error is 0.16 meters, therefore, the expected cumulative
error is 0.49 m. The variance of the sum of two or more random variables is
equal to the sum of the variances when the random variables are independent -
as selection and measurement errors are assumed to be. In this case, the
expected variance of selection error is 0.11 m and the expected variance of
measurement error is 0.77 m, therefore the expected variance of cumulative error
is 0.88 m. To complete my illustration, Figure 5.4 shows a histogram of 529
simulated cumulative errors in paleoshoreline elevations.

It is assumed that paleoshoreline elevation data contain relatively small
cumulative errors that are spatially unstructured. At this time, the best estimate
of error at any location is the expected cumulative error (0.49 m), so 0.49 m was

subtracted from each observed paleoshoreline elevation value.

196

80

60

40

Frequency (11)

20

 

-4 —2 0 2 4
Cumulative error (m)
(a)
Figure 5.4: Histogram of cumulative paleoshoreline elevation errors. Error

values are binned in 0.25 m intervals. Frequency scale is different than that used
in Figure 5.2.

Models of differentially upwarped water planes

My data are sufficient to support reconstructions of four glacial Lake
Algonquin water planes: Main, Ardtrea, Upper Orillia and Lower Orillia. The
later three are known as the ”Upper Group” (after Deane, 1950). Field evidence
exists for several lower, and presumably younger, water planes in Ontario and
the Upper Peninsula (e. g., Penetang, Cedar Point and Payette). Although I
discuss the Cedar Point phase briefly, I do not have enough data to support a
reconstruction or enough data to support reconstructions of any phase belonging
to the ”Lower Group” (after Stanley, 1936).

Water plane elevations are modeled as a random field:

197

thase(u) : mphase(u) "I" 5'phase (‘0 + gt'phase (u)! Vu e R [Eq_ 21]

where: phase denotes the Main, Ardtrea, Upper Orillia or Lower Orillia water

plane, mphasem) represents the expected elevation trend of that plane; 5'phase (u)

represents random and spatially-structured deviations from the uplift trend; and

8"phase (u) represents random and spatially unstructured errors.

It is reasonable to model upwarped water planes as random fields because
each water plane can be considered in terms of the three components of a
random field. As discussed previously, former water planes are differentially
upwarped in a manner that elevation increases ”exponentially toward the former
ice centers” (Larsen, 1987: p11). The regional uplift pattern can be modeled as an
elevation trend with a non-stationary mean elevation. Localized deviations from
the regional trend are associated with differences among site conditions.
Goldthwait (1908), for example, allowed for ”five feet" (1.5 m) of discordance for
”original variations in height due to local conditions under which [relict
shoreline features - author’s inclusion] were constructed or cut” (p.463).
Alternatively, localized deviations from the general water-plane trend can be
modeled as random and spatially-structured covariations. And finally,
unexplained or chaotic deviations from the combination of the global trend and

regional structure components can be captured by a random and spatially

198

unstructured error component. Chapter 2 describes short-term and cyclic
influences that effect random and chaotic behavior in water-levels.

Water planes were reconstructed initially using the general spatial
prediction protocol outlined by Bailey and Gatrell (1995:189-190). The protocol
stipulates: a) fit a suitable trend surface model to data using ordinary least
squares and obtain residuals; b) if residuals evince spatial structure, then conduct
a variography and select a suitable variogram model to capture the structure; c)
re-fit a suitable trend surface model to data using generalized least squares to

accommodate both the spatial trend component [mphase(u) ]and the random and
spatially structured error component [e'phase (u) l; d) examine the new set of
residuals [6" phase (u)] for anomalies or any remaining spatial structure; and, if

needed, e) iterate through steps b and c until stability is achieved.

Universal kriging is mathematically similar to the general spatial
prediction protocol outlined above, except the set of trend parameters are
estimated implicitly ”and not made explicit in the results” (Bailey and Gatrell,
1995: 196). I made the modeling decision to use universal kriging during the
final model run because I am most interested in the final prediction surface and,
for now, less interested in the parameters that describe uplift. This decision also
allowed me to take advantage of the variography and cross-validation

assessment tools already available in the geoR (Ribeiro and Diggle, 2001) and

199

gstat (Pebesma, 2004) packages made for the R environment for statistical
computing (R Development Core Team, 2005).

Isaaks and Srivastava (1989) and Bailey and Gatrell (1995) suggest using
cross-validation to assess spatial prediction models for dangerous warning signs
before proceeding onto a final model run. Bailey and Gatrell provide a concise

summary:

”Each sample point is deleted in turn and its value predicted
from the rest of the data, using the chosen variogram model and
the chosen form of the trend component. This results in an
observed set of n prediction errors between the predicted and true
values at each sample site. These prediction errors can then be
studied in order to evaluate the overall prediction process and
possibly identify necessary adjustments to either the variogram

model or the form of the trend.” (Bailey and Gatrell, 1995: 191)

I employed cross-validated universal kriging to get a sense of how well
(or poorly) each ad-hoc combination of trend, spatial structure, and aspatial
noise components behaved. I examined cross-validated residuals for large
errors, bias and any remaining spatial structure. If I found such evidence, then I
would review data for any rnisclassified features and return to the spatial
prediction protocol. According to Isaaks and Srivastava (1989), cross-validation

provides a valuable ”dress rehearsal” (p533) for a final model run because it can

200

identify poor model performance. They warn, however, that cross-validation
does not guarantee best model performance and should be used cautiously when
adjusting a variogram model. In this work, if a dress rehearsal did not reveal
dangerous warning signs, then I proceeded to a final run and reconstructed the
differentially warped water plane via universal kriging. I report only the set of

final water plane models.

A note about coordinate transformation

Before reporting my final water plane models, however, I note that all
coordinate values were transformed from the Michigan GEOREF planar
coordinate system to a local coordinate system. Coordinate transformation
involved rescaling from the meter to the kilometer unit of measure, and
translating the origin from outside the State of Michigan to a location at Traverse
City, Michigan. I rescaled coordinate values after building an initial set of
models and obtaining unstable results (not reported). Although my initial
models seemed reasonable at first, I found they suffered from rounding errors
created by computer word overflows (Burrough and McDonnell, 1998: see Box
9.2 on page 228) - especially when coordinate values were raised to powers
greater than 1 during trend surface analysis. Translation of the origin to Traverse
City, MI serves two purposes. First, it reduces further the magnitudes of values
needed to represent bluff locations and, so, further mitigates problems associated

with computer word overflows. And second, it places the origin inside the study

201

area, which allows the intercept term of each trend surface model to serve as a
useful, rather than useless, estimate of water plane elevation. Locations in
Traverse City were not sampled during this work, so placing a false origin there

conveniently allows water plane elevations to be predicted at the site.

Main phase
The spatial distribution of Main water plane elevations is modeled as a

random field {H mam(ui ),u,- e R}, which is a set of spatially-structured random
variables { H main (ul- ),i = 1,...,N} each defined at the center of one of N grid cells in
the region of interest R. The set of sampled paleoshoreline elevations associated
with the Main phase of glacial Lake Algonquin {hmm-n (u a ), a = 1,..., n} is
considered one possible realization of 11 corresponding random variables. The

set of 59 samples I assembled lhmain (u a ),a = 1,...,59} is considered a joint

realization of 59 corresponding random variables.
Polynomial trend surface models were fit to elevation data via ordinary

least squares (OLS) to capture the expected northeastward trend mmain (u).

Trend models were checked for goodness of fit and overall significance.
Parameter coefficients were tested for significance, and outliers and observations
that might have unduly leveraged results were removed. Ultimately, a reduced
second-order polynomial provided the best statistical fit (Table 5.1). Coefficients

of the y2 and interaction (x*y) parameters are both positive in sign and support

202

the expectation that water plane elevations increase toward the northeast. A
summary of residuals is listed in Table 5.2.

OLS residuals are generally small and well-behaved (e. g., non-normality
was not evident, they were not correlated with predicted values or independent
variables), but they exhibit spatial structure (maps used for rummaging through

these data are not shown).

Table 5.1: Main phase trend parameters estimated via ordinary least squares.

 

OLS Estimate Standard error Probability
Intercept 212.3 1.3 < 0.0001

ka -0.2405 0.0260 < 0.0001

ka* Ykm 0.001838 0.0001 < 0.0001

ka2 0.001213 0.0001 < 0.0001

ykm2 0.001743 < 0.0001 < 0.0001

Adjusted R2 0.9930

F-statistic 1973

p-value < 0.0001

Residual standard error 2.01 m

Table 5.2: Summary of Main surface residuals obtained via ordinary least
squares (OLS), cross-validated universal kriging with a nugget model only
(CV.NUG), and cross-validated universal kriging with a Matern model of spatial
structure (CV .MAT).

 

Residuals OLS CV.NUG CV.MAT
minimum -3.66 m -4.17 m -3.14 m

median -0.18 m 0.19 m -0.26 m

mean (bias) 0.00 m 0.04 m 0.00 m
RMSE 1.92 m 2.12 m 1.66 m

maximum 4.54 m 4.77 m 3.43 m

203

A variography revealed an anisotropic association between semi-variance
and distance. 2 The strongest spatial correlation structure occurs along an
azimuth of 20 degrees (Figure 5.5a). No spatial structure is apparent along an
azimuth of 110 degrees (Figure 5.5b). Not incidentally, the axis of strongest
spatial structure coincides with the general direction of glacial retreat (N15°E,
after Futyma, 1981). Such a coincidence might suggest the trend model does not
capture the uplift trend completely. Yet, semi-variance along this axis does not
increase monotonically with distance, which suggests a localized process, and
not a global process, is acting. Semi-variance values reach a sill between the 20
and 30 km lags, beyond which no spatial structure is apparent. The ad-hoc
division of large-scale trend, smaller-scaled spatial structure, and aspatial noise,
seems reasonable, so I moved forward.

I did not fit a trend to data via generalized least squares because I could
not build a suitable anisotropic covariance matrix. Instead, I relied on the cross
validation tools available in the gstat package, which can accommodate
anisotropic spatial structures. I assessed two water plane models via cross-

validated universal kriging. The first employed the global trend and an aspatial

 

2 All semi-variograms were calculated using 4 km lags, or bins, and constrained to a
minimum of 6 pairs of observations in each lag. Directional variograms were calculated
using a 45-degree tolerance angle. Efforts to assess semi-variance at distances shorter
than 4 km proved futile because I could not capture sufficient numbers of paired

observations in every lag or obtain interpretable results.

204

noise component (pure nugget). The other employed the global trend, an
anisotropic variogram model of spatial structure and an aspatial noise
component (Figure 5.5). Comparing sets of residuals generated by these two
universal kriging models allowed me to asses whether or not the anisotropic

spatial component served to better the prediction process.

 

 

 

 

15 j n: 59
8 C;
1: 10 Model: Matern
.‘2 '
a :
2 Sill: 3.5 m2
E 5 .
a) .
m Range: 19 km
0
0 10 20 30 40 50 60 Kappa: 0'5
Distance (km) Nugget: 2.2
a) 20 degrees azimuth
15";
m
8 10 l
0% n: 59
.2 ,
E 5 , .
8 1 Model. Pure nugget
0': ._ ,. ,. . Nugget:2.2
0 10 20 30 40 50 60
Distance (km)
b) 110 degrees azimuth

Figure 5.5: Empirical variograms of Main trend surface residuals generated via
ordinary least squares. Solid lines represent fitted variogram models.

205

Neither kriging model generated residuals that evince bias, extreme
values, or warning signs that suggests the trend model should be refined further.
The model that employed only the aspatial noise component generated the
largest residuals. The model that employed both anisotropic covariance and
aspatial noise components performed best and generated residuals smaller than
those generated via OLS, which suggests the model compensated for missing
data and offers good predictive ability.

I reconstructed the final Main glacial Lake Algonquin water plane via
universal kriging using the anisotropic variogram model described above.
Figure 5.6a shows the final prediction surface, which illustrates the uplift trend
toward the former center of ice loading. Figure 5.6b shows the surface of
confidence intervals (at the 95% confidence level) about the predictions. The
spatial pattern of uncertainty reflects the distribution of available data for
confidence intervals tend to increase with distance from sampled locations.

Note, there are no data to support the curve expressed by the 210 m contour line.

206

 

    

 

 

 

.\i l

(a) Predicted elevations (b) Uncertainty in the predictions

Figure 5.6: The Main Lake Algonquin water plane: a) predicted elevations are
contoured with a 10-meter interval; and b) greater uncertainties are expressed
with darker gray tones. Sample sites are shown as black dots.

Ardtrea phase

The spatial distribution of Ardtrea water plane elevations is modeled as a
random field {H ard(u,- ), ul- 6 R}, which is a set of spatially-structured random
variables {H a,d(u,-),i = 1,...,N} each defined at the center of one of N grid cells in
the region of interest R. The set of paleoshoreline elevations associated with the
Ardtrea phase of glacial Lake Algonquin {hard(ua),a = 1,...,n} is considered one

possible joint realization of 11 corresponding random variables. The set of 41

samples I assembled {ha,d(ua),a = 1,...,41} is considered a joint realization of 41

corresponding random variables.

207

Trend surface models were fit to data via ordinary least squares to capture

the expected uplift trend m “m(u). Models were checked for fitness and

significance, coefficients were assessed for significance, and residuals were
examined thoroughly. Ultimately, a reduced second-order polynomial model
provided the best fit (Table 5.3). It is worth noting that the general form of the
Ardtrea model is the same as the form of the Main model - only the parameters
that specify rates of uplift are different. For example, the Ardtrea intercept (208.3
m) is lower than the Main intercept (212.3 m), which suggests the Ardtrea water
plane is below the Main water plane at Traverse City. Also, each rate of uplift in
the Ardtrea trend model is less than its respective counterpart in the Main trend
model, which indicates the Ardtrea water plane is warped less than the Main
plane. A summary of residuals is listed in Table 5.4. OLS residuals are small and
well behaved (e. g., non-normality is not evident, they are not correlated with
either sets of predicted values or independent variables), and they evince no
spatial structure (maps used for rummaging through these data are not shown).

I conducted a variography to explore the spatial structure of OLS residuals (e. g.,
Figure 5.7), but found none.

I calculated an inter-distance matrix and used a pure nugget variogram
model to convert it into a covariance matrix. The trend surface model was then
re-fit to data via generalized least squares; the inverse of the covariance matrix
was used as a spatial weights matrix. Model parameters are organized in Table

5.3 and a summary of residuals is given in Table 5.4. As expected, the

208

generalized model provides a fit identical to the ordinary model. The pure
nugget component does not alter the overall fit or significance of the model;
rather, it inflates the standard error associated with each parameter estimate.

Nevertheless, all coefficients remain significant at the 95% confidence level.

Table 5.3: Ardtrea phase trend parameters estimated via ordinary least squares
(OLS), and generalized least squares (GLS).

 

 

OLS Estimate Standard error Probability
Intercept 208.3 0.9 < 0.0001

ka -0.2008 0.0201 < 0.0001

ka* y1<m 0.001645 < 0.0001 < 0.0001

ka2 0.001026 < 0.0001 < 0.0001

ykm2 0.001667 < 0.0001 < 0.0001

Adjusted R’- 0.9961

F-statistic 2547

p-value < 0.0001

Residual standard error 1.42 m

GLS Estimate Standard error Probability
Intercept 208.3 1.3 < 0.0001

ka -0.2008 0.0273 < 0.0001

ka" ykm 0.001645 0.0001 < 0.0001

ka2 0.001026 0.0001 < 0.0001

ykm2 0.001667 < 0.0001 < 0.0001

Adjusted R2 0.9961

F-statistic 2547

p-value < 0.0001

Residual standard error 1.42 m

209

Table 5.4: Summary statistics for residuals (n=41) obtained from Ardtrea water
plane models predicted via ordinary least squares (OLS), generalized least
squares (GLS), and cross-validated universal kriging (CV .NUG).

 

 

Residuals OLS GLS CV.NUG
minimum -2.73 m -2.73 m -2.96 m
median 0.03 m 0.03 m 0.04 m
mean (bias) 0.00 m 0.00 m -0.01 m
RMSE 1.33 m 1.33 m 1.55 m
maximum 2.82 m 2.82 m 3.35 m
15 i n: 41
8 Model: Nugget
E 10
g Nugget: 2.1
E 5
a)
i T :13: w W 11 "r it".
0 10 20 30 40 50 60

Distance (km)

Figure 5.7: Empirical variogram model fitted to the spatial structure of Ardtrea
water plane residuals generated during ordinary least squares.

The Ardtrea model was assessed via cross-validated universal kriging,

which generated a set of residuals with characteristics similar to those generated

via least squares, albeit with a larger range. Cross-validated residuals do not

evince bias, extreme values, spatial structure or any warning sign that might

suggest either the trend component or the noise component should be refined

further. The average magnitude of error (RMSE = 1.55 m) is small. So, I accepted

the ad-hoc division of trend and aspatial noise and moved forward.

210

I reconstructed the Ardtrea water plane from paleoshoreline data via
universal kriging and included a pure nugget model of aspatial noise. Figure
5.8a shows the final prediction surface, which illustrates the uplift trend toward
the northeast. Figure 5.8b shows the surface of confidence intervals (at the 95%
confidence level) about the predictions. The spatial pattern of uncertainty
reflects the distribution of available data for confidence intervals tend to increase
with distance from sampled locations. Locations in the southwestern portion of
the study area suffer the greatest uncertainties because they are situated farthest

from data.

 

 

 

 

 

   

 

 

 

 

 

 

1
u...’ ....... . .-. ...-... .5
1 , l ‘

(a)Predicted elevations I (b) Uncertainty in the predictions

   

1
I

 

Figure 5.8: The Ardtrea phase water plane: a) predicted elevations are contoured
with a 10-meter interval; and b) greater uncertainties are expressed with darker
gray tones. Sample sites are shown as black dots.

211

Upper Orillia phase
The spatial distribution of Upper Orillia water plane elevations is

modeled by a random field {H on- (u,- ), u,- e R} , which is a set of spatially-
structured random variables {H on- (ui ),i = 1,..., N} each defined at the center of

one of N grid cells in the region of interest R. The set of paleoshoreline
elevations associated with the Upper Orillia phase of glacial Lake Algonquin

{hm (u a ), a = 1,..., n} is considered one possible joint realization of 11

corresponding random variables. The specific set of 33 samples I collected

{hon- (u a ),a = 1,...,33} is considered a joint realization of 33 corresponding

random variables.
Trend surface models were fit to data via ordinary least squares to capture

the expected trend mon- (u). Trend models were checked for fitness and

statistical significance, and residuals were explored for outliers and evidence of
undue leverage. Ultimately, a reduced second-order model provided the best fit
(Table 5.5). The general form of the Upper Orillia model is the same as the
general form of the Main and Ardtrea models - only the parameter estimates are
different. For example, the Upper Orillia intercept (199.9 m) is lower than the
Main intercept (208.3 m), which suggests the Orillia water plane is below the
Ardtrea water plane at Traverse City. Also, each rate of uplift in the Orillia trend

model is less than its respective counterpart in the Ardtrea trend model, which

212

indicates the Upper Orillia water plane is warped less than the Ardtrea (and
hence Main) water plane. A summary of residuals is listed in Table 5.6.

OLS residuals behaved well (e.g., non-normality not evident, not
correlated with either sets of predicted values or independent variables), but
they exhibited spatial structure. I conducted a variography to explore the
apparent autocorrelation, which exposed a substantial anisotropic spatial
structure. And, unlike the variograms calculated for the Main and Ardtrea
residuals, these reveal a lot of scatter. After iteration, reasonable variogram
models were fit by eye (Figure 5.9).

I did not fit a trend surface model to data via generalized least squares
because I could not build a suitable anisotropic covariance matrix for use in a
generalized linear model. Again, I relied on the tools available in the gstat
package, which can accommodate such anisotropic structures. I assessed two
water plane models via cross-validated universal kriging. The first employed the
global trend and an aspatial noise component (pure nugget). The other
employed the global trend, an anisotropic spatial component, and an aspatial
noise component. Comparing sets of residuals generated by these two universal
kriging models allowed me to asses whether or not the anisotropic spatial

component served to better the prediction process.

213

Table 5.5: Upper Orillia phase trend parameters estimated via ordinary least
squares.

 

OLS Estimate Standard error Probability
Intercept 199.9 1.5 < 0.0001

ka -0.1442 0.0412 0.0002

ka* Ykm 0.001433 0.0009 < 0.0001

ka2 0.000917 0.0002 0.0001

ykm2 0.001623 < 0.0001 < 0.0001

Adjusted R2 0.9900

F-statistic 793.4

p-value < 0.0001

Residual standard error 2.69 m

Table 5.6: Summary statistics for residuals (n=33) obtained from Upper Orillia
elevation trend models obtained via ordinary least squares (OLS), cross-
validated universal kriging with pure nugget model (CV.NUG) and cross-
validated universal kriging with anisotropic covariance model (CV.MAT).

 

Residuals OLS CV.NUG CV.MAT
minimum -4.76 m -5.07 m -3.81 m

median 0.34 m 0.42 m 0.54 m

mean (bias) 0.00 m 0.09 m 0.11 m
RMSE 2.48 m 2.95 m 1.88 m

maximum 4.50 m 6.01 m 4.28 m

Neither universal kriging model generated residuals that evince bias,
extreme values, or other warning signs that suggests the trend model should be
refined further. The model that employed only an aspatial noise component
generated the largest residuals. The model that employed both anisotropic

covariance and aspatial noise components, however, performed best and

214

generated residuals smaller than those generated via OLS, which suggests the

model compensated for missing data and offers good predictive ability.

 

 

15' n: 33
8 .
c 10 Model: Matern
.9
(Ti
.2 ‘ Sill: 9.5 m2
E 5
c)”, g
Range: 30 km
0.
0 20 40 60 80 100 120 Kappa:0'5
Distance (km) Nugget: 0.5 m2
a) 20 degrees azimuth
15-__ n: 33
8
1: 10 Model: Matern
.9 -
a :
.2 ,_ Sill: 9.5 m2
E 5'
(D :
m Range: 60 km
0
0 20 40 60 80 100 120 19139305
Distance (km) Nugget: 0.5 m2
b) 110 degrees azimuth

Figure 5.9: Spatial structure of residuals obtained during attempts to model the
Upper Orillia water plane via ordinary least squares.

215

I reconstructed the Upper Orillia water plane from paleoshoreline data via
universal kriging using the anisotropic variogram model described above.
Figure 5.10a shows the final prediction surface, which shows the expected
pattern of increasing elevation toward the former center of ice loading. Figure
5.10b shows the surface of confidence intervals about the predictions (at the 95%
confidence level). Again, darker tones express confidence larger intervals and,
hence, greater uncertainties.

It is worth noting the Upper Orillia water plane is supported by fewer
data than those that support the Main or Ardtrea water planes, but Upper Orillia
data span a greater geographic extent. Perhaps that is why, of the three, the
Upper Orillia model is noisiest, least precise, and subject to the greatest
uncertainties. Also, possible classification errors regarding closely-spaced Upper
Orillia and Lower Orillia features might play a role. Nevertheless, the Upper

Orillia water plane model is the best model I can build with these data.

216

 

 

1 0
(a) Predicted elevations (b) Uncertainty in the predictions

  

 

 

 

 

 

 

Figure 5.10: The Upper Orillia phase water plane: a) predicted elevations are
contoured with a 10-meter interval; and b) greater prediction uncertainties are
expressed with darker gray tones. Sample sites are shown as black dots.

Lower Orillia phase

The spatial distribution of Lower Orillia water plane elevations is
modeled as a random field {H low (ui ),ui e R] , which is a set of spatially-
structured random variables {H low (ui ),i = 1,...,N} each defined at the center of
one of N grid cells in the region of interest R. The set of paleoshoreline
elevations associated with the Lower Orillia phase {hjow(ua ), a = 1,...,n} is

considered one possible joint realization of n corresponding random variables.

The specific set of 16 samples I assembled {hlow(ua),a = 1,...,16} is considered a

joint realization of 16 corresponding random variables.

217

Initial trend surface models were fit to data via ordinary least squares to

capture the expected trend component m [m(u) in these data. Trend surface

models were checked for fitness and significance, significant coefficients, outliers
and observations that might have unduly leveraged the results. Ultimately, a
reduced second-order model provided the best fit (Table 5.7). A summary of

residuals is listed in Table 5.8.

Table 5.7: Lower Orillia phase trend model parameters estimated via ordinary
least squares (OLS), and generalized least squares (GLS).

 

 

OLS Estimate Standard error Probability
Intercept 194.4 0.8 < 0.0001

ka -0.3614 0.0434 <0.0001

ka*Ykm 0.001463 < 0.0001 < 0.0001

kaz 0.002026 0.0002 < 0.0001

ykm2 0.001862 < 0.0001 < 0.0001

Adjusted R2 0.9979

F-statistic 1760

p-value < 0.0001

Residual standard error 1.42 m

GLS Estimate Standard error Probability
Intercept 194.4 1.0 < 0.0001

ka -0.3614 0.0531 <0.0001

ka*ykm 0.001463 < 0.0001 < 0.0001

ka2 0.002026 0.0003 < 0.0001

y1<m2 0.001862 < 0.0001 < 0.0001

Adjusted R2 0.9979

F-statistic 1760

p-value < 0.0001

Residual standard error 1.42 m

218

Table 5.8: Summary statistics for residuals (n=16) obtained from Lower Orillia
water plane models predicted via ordinary least squares (OLS), generalized least
squares (GLS) and cross-validated universal kriging (CV.UK).

 

Residuals OLS GLS CV.UI<
minimum -2.37 -2.37 -3.43

median -0.03 -0.03 -0.05

mean (bias) 0.00 0.00 -0.01
RMSE 1.18 1.18 1.83

maximum 2.10 2.10 3.98

The initial set of OLS residuals behaved well (e. g., non-normality not
evident, not correlated with either set of predicted values or independent
variables), which is not surprising given that a five-term surface model was fit to
16 points. A variography revealed no pattern of spatial autocorrelation among
residuals (Figure 5.11). The small number of observations made variography

difficult, but a pure nugget model was fit by eye to capture the apparerlt noise.

 

15 g n: 21
8 I Model: Nugget
w :
g j Nugget: 1.5
E 5 1
m .
U) : A -
o 5

O 10 20 30 40 50 60
Distance (km)

Figure 5.11: Spatial structure of OLS residuals generated during attempts to
model the Lower Orillia water plane.

219

I calculated an inter-distance matrix and used the pure nugget variogram
model to transform it into a covariance matrix. The trend surface model was
then re-fit to data via generalized least squares; the inverse of the covariance
matrix was used as a spatial weights matrix. Model parameters are organized in
Table 5.7 and a summary of residuals is given in Table 5.8. As expected, the
generalized model provides a fit identical to the ordinary model. The pure
nugget component does not alter the overall fit or significance of the model;
rather, it inflates the standard error associated with each parameter estimate.
Nevertheless, all coefficients remain significant at the 95% confidence level.

The Lower Orillia model was assessed via cross-validated universal
kriging, which generated a set of residuals with characteristics similar to those
generated via least squares, albeit with a larger range. A larger range was
expected given the relative paucity of data and extent they cover. Cross-
validated residuals do not evince bias, extreme values, spatial structure or any
other warning sign that might suggest the trend component should be refined. I
accepted the ad-hoc division of trend and aspatial noise and moved forward.

I reconstructed the Lower Orillia water plane from paleoshoreline data via
universal kriging and using only a pure nugget model of aspatial noise. Figure
5.12a shows the final prediction surface, which illustrates the uplift trend toward
the northeast. Figure 5.12b shows a surface of uncertainty in the predictions.
The spatial pattern of uncertainty reflects the distribution of available data for

uncertainty increases with distance from sampled locations.

220

         

L..._.__ x "

(a) Predicted elevations” -» (b) Uncertainty in the predictions
Figure 5.12: The Lower Orillia phase water plane: a) predicted elevations are

contoured with a 10-meter interval; and b) greater prediction uncertainties are
expressed with darker gray tones. Sample sites are shown as black dots.

Cedar Point phase

Fourteen relict bluffs are associated with the Cedar Point water plane and
all are located in the northern reaches of the study area. The number and
geographic distribution of these data are insufficient to support a water plane
reconstruction that covers the entire study area. Nevertheless, I was curious to
explore all that these data might allow.

Trend surface models were fit to data via ordinary least squares in an
attempt to capture the expected trend. Trend models and their residuals were
assessed in the usual way. Ultimately, a first-order trend provided the best fit

(Table 5.7). A first-order trend model cannot and does not reflect the increasing

221

rate of uplift that is expected among these data. Perhaps there is too much noise
among them, or perhaps these data are not distributed broadly enough to
capture such a non-linear trend. What can be gleaned, however, it that the rate
of uplift is greater toward the north than toward the east. The intercept term,
albeit a far-reaching extrapolation, suggests the Cedar Point wateroplane projects
far below the contemporary land surface at Traverse City. This estimate is not
supported by any observation at or near Traverse City, but is does correspond
with the generally held expectation that water planes of the ”Lower Group,” like
the Cedar Point water plane, represent phases in the transition from high glacial

Lake Algonquin waters to the Chippewa lowstand.

Table 5.7: Cedar Point phase trend parameters estimated via ordinary least
squares (OLS).

 

OLS Estimate Standard error Probability
Intercept 47.2 6.0 < 0.0001

ka 0.3879 0.0164 <0.0001

ykm 0.8485 0.0261 < 0.0001

Adjusted R2 0.9872

F-statistic 538.8

p-value < 0.0001

Residual standard error 1.57 m

222

Models of errors in the digital elevation model

A digital elevation model (DEM) contains errors in elevation that are
results of imprecise sampling, measurement and interpolation processes (see e. g.,
Shortridge, 2001; Fisher, 1998; Bolstad and Stowe, 1994; Brown and Bara, 1994
and Shearer, 1990). The DEM employed in this work has suffered these as well
as map projection and resampling processes that have introduced other errors.
Interpolation and resampling processes are generally known to reduce variation
in elevation data by trimming local extrema (Burrough and McDonnell, 1998).
These effects have spatial consequences for they render an artificially smooth
surface that underestimates local maxima and overestimates local minima
(Diggle and Ribeiro, 2002). This kind of information suggests the distribution of
DEM error should exhibit some form of spatial continuity or structure. And
indeed, the DEM employed in this work exhibits spatial structure.

I continued to handle the DEM using the three subsets (i.e., Lower
Peninsula, Upper Peninsula and Ontario) described in Chapter 4 because each
subset exhibits different error characteristics (Table 4.6), each contains data
derived from different measurement processes, and doing so facilitated
computation Within the memory limits of a Microsoft Windows environment. In
addition, the central upland region within Michigan’s Lower Peninsula was
masked from analysis because the region is clearly not associated with glacial
Lake Algonquin features, for the land surface rests at elevations much higher

than the highest known glacial Lake Algonquin plane, and doing so reduced

223

further the computer memory requirements associated with manipulating the
large subset.

The spatial distribution of surface elevations within the study area is
modeled as a random field {Y(u,-), u} E R}, which is a set of spatially-structured
random variables {Y(u,'), i = 1, . . .,N} each defined at the center of one of N grid
cells {u., i = 1,. . .,N} in the region of interest R. A DEM {y(ui), i = 1,...,N} is
considered one possible realization of the random field {Y(ui), u.- e R}, or one
possible joint realization of N random variables {Y(u.'), i = 1, . . .,N}. Specifically,
the DEM described in Chapter 4 {1/(Ua), a= 1, . . .,25718215} is considered one
possible joint realization of 25,718,215 corresponding random variables.

The spatial distribution of control point elevations is modeled by a second
random field {Z(ui), u.- e R}, which is a set of spatially structured random
variables [Z(Ui), i = 1,. . .,N} with each defined at the center of one of N grid cells
{u., i = 1, . . .,N} in the region of interest R. In general, a set of 71 control point
elevations {Z(ua), a = 1, . . .,n} is considered a joint realization of n random
variables. Specifically, the set of 529 control point elevations described above
{Z(ua), a = 1,. . .,529} is considered one possible joint realization of 529
corresponding random variables.

The relation between these two random fields {Y(u,-), u,- E R} and {Z(ui), u.-

E R} can be expressed (following the example given by Kyriakidis et a1, 1999) by:

Y(u,-) = Z(u.) + B(u.~), v u.- e R [Eq. 22]

224

where {B(ug), ui E R} is a third random field that is used to model the spatial
distribution of error in the DEM. In this case, it is a set random variables {3011), i
= 1, . . .,N} and each is defined at the center of one of N DEM grid cells {111, i =
1,. . .,N} in R. In general, a set of n elevation errors estimated at control point
locations {b(ua), a = 1,. . .,n} is considered a joint realization of 11 random variables.
Specifically, the set of 529 error values described above {b(ua), a = 1,. . .,529} is
considered a joint realization of 529 corresponding random variables.

The spatial distribution of DEM error B (u) can then be expressed in terms

of a random field:

B(u) = m3(u) + eB'(u) + 53” V u e R [Eq. 23]

where B(u) is the random field, m3(u) is the expected value or trend component,
£3’(u) is the random and spatially structured error component, 53” is the random

and spatially unstructured error component, and u is the set of all locations in R.

Variography

DEM errors exhibit apparent spatial structure (Figure 4.8). A semi-
variogram is a measure of variability and useful for exploring spatial structure in
data. Semi-variogram calculations require data that are distributed as Normal
(Goovaerts, 1998). Non-normal data can be transformed to normally-distributed
standard scores, analyzed, and then back-transformed when original units are

required. Results of Shapiro-Wilk tests for normality indicated the distributions

225

of error in the Lower Peninsula and Upper Peninsula subsets do not fit a Normal
distribution. So, power transformations were applied to both subsets and each
was transformed again into standard normal scores. Results of a Shapiro-Wilk
test for normality indicated the distribution of error in Ontario does resemble a
Normal distribution, so these values were simply transformed once to standard
normal scores.

Semi-variogram calculations are ”unacceptable” for ”distances larger than
half the extent of the area” of interest (Omre, 1984:107), so I plotted my
calculations accordingly. Figure 5.13 shows empirical omni-directional semi-
variograms and the models I chose to capture spatial structure in each subset. I
chose to fit all models from the Matern class of correlation functions (Minasny
and McBratney, 2005 and Stein, 1999). Unlike the more familiar function classes
found in textbooks (e. g., Gaussian, spherical, exponential or linear), the Matern
class offers flexibility for fitting spatial covariance structures because it utilizes a
fourth smoothing parameter (kappa) in addition to the standard sill, range and

nugget parameters.

226

Semivariance
O

2.0 -

Semivariance

0.0

2.0

0.5

Semivariance

0.0

1.5;
1.0“

0.5 4

1.5'

1.0 --

10

 

10

 

20 30

Distance (km)

(a) Lower Peninsula subset

20 30

Distance (km)

(b) Upper Peninsula subset

2

i
it
i:
i

3 4

Distance (km)

(c) Ontario subset

 

40

40

n: 348

Model: Matern
Sill: 1.00
Range: 2.0 km
Nugget: 0.35

Kappa: 0.7

n: 108

Model: Matern
Sill: 1.00
Range: 2.0 km
Nugget: 0.20

Kappa: 1.4

n: 73

Model: Matern
Sill: 1.00
Range: 0.15 km
Nugget: 0.28

Kappa: 5.0

Figure 5.13: Empirical semi-variograms and variogram models for DEM subsets.

227

I calculated directional semi-variograms for each subset (not shown), but
they provided no evidence of either geometric or zonal anisotropy. Moreover,
directional variogram calculations yielded erratic results that were difficult to
interpret consistently - especially at shorter distances, so I relied on omni-
directional calculations only. Not incidentally, Isaaks and Srivastava (1989)
warned that spatial continuity analysis is ”very frustrating, sometimes seemingly
hopeless” (p140), rarely straightforward and can often require several iterations.
I am satisfied with my results, but found no reason to believe Isaaks and
Srivastava’s were crying ”wolf.”

A semi-variogram of errors in the Lower Peninsula region (Figure 5.13a),
which is supported by a relatively large number of observations (n = 348),
exhibits a pattern of decreasing correlation (increasing semi-variance) at
relatively short distances (< 7 km) and no apparent correlation structure at
distances greater than 10 km. A Matern variogram model (nugget = 0.35, sill =
1.0, range = 2.0 km and kappa = 0.7) was fit by eye. Efforts to better model semi-
variance using small bins (< 300 m) and short distances (< 1 km) proved futile
because I could not capture sufficient numbers of paired observations or obtain
stable and interpretable results.

A semi-variogram of errors in the Upper Peninsula region (Figure 5.13b),
which is supported by 108 observations, exhibits a pattern of increasing semi-
variance at relatively short distances (< 10 km) and no apparent correlation

structure at distances greater than 10 km. A single Matern variogram model

228

 

(nugget = 0.2, sill = 1.0, range = 2.0 km and kappa = 1.4) was fit by eye to capture
the observed spatial structure in the region. As is obvious from Figure 5.13b,
semi-variogram calculations at relatively short distances scatter rapidly and, so,
are relatively difficult to model. Efforts to better model semi-variance at short
distances again proved futile because I could not capture sufficient numbers of
paired observations within small bins or obtain suitably stable and interpretable
results. The apparent nugget effect (0.2) is, however, lower than that observed in
the Lower Peninsula (0.35), probably because much of the Upper Peninsula
exhibits flatter terrain.

Error observations in Ontario are relatively few (11 = 73) and highly
clustered, which facilitated efforts to model spatial structure among short
separation distances but impeded attempts to model spatial structure among
longer distances. The semi-variogram of error in the Ontario region (Figure
5.13c) exhibits a pattern of increasing semi-variance at relatively short distances
(< 1 km). A single Matern variogram model (nugget = 0.28, sill = 1.0, range =
0.15 km and kappa = 5.0) was fit by eye to best capture the observed spatial
structure. The large kappa parameter allowed for the best fit between model and
empirical data, but required use of a range parameter (150 m) that

underestimates the apparent effective range (~1 km).

229

Making predictions

I used the error samples and variogram models described above, and the
ordinary kriging tools available in gstat (Pebesma, 2004), to predict error
distributions and generate error surfaces for the Lower Peninsula, Upper
Peninsula, and Ontario regions. I then used GIS software to build a composite
surface of predicted DEM errors for the study area (Figure 5.14).

Visualizing the composite error surface can reveal differences among
subsets that have been described already with prose and statistic. For example,
the spatial structure among sampled errors in the Lower Peninsula subset has a
lesser effective range than that which was observed among sampled errors in the
Upper Peninsula. The quantitative difference is expressed visually as relatively
small zones of influence around sampled benchmark locations in the Lower
Peninsula and relatively large zones of influence in the Upper Peninsula.
Differences among mean error values are also evident. Mean errors in the Lower
Peninsula (-0.06 m) and Upper Peninsula (-0.50 m) subsets are near zero.
Ordinary kriging tends toward the sample mean when predicting values at
unsampled locations that are situated far from sampled locations and beyond the
effective range of spatial dependence. Such predictions are symbolized in Figure
15.3 with a pale gray tone. The average magnitude of error in the Ontario subset
(-1.58 m) is larger, which is why locations in Ontario that are situated far from
sampled locations and beyond the modeled range of spatial dependence are

shown conspicuously, in Figure 5.14, with a pinkish hue.

230

 

 

Predicted error value (m)
u 3.1 to 14.7
12:3 1.1 to 3.0
C3 .10 to 1.0
C3 -2.9 to -1.1 .
u -9.9 to -3.0 '.

 

 

 

 

 

 

 

 

Figure 5.14: Composite surface of predicted DEM errors. The image in this
dissertation is presented in color.

I built a composite surface of ordinary kriging variances, which ultimately
I transformed into a surface of confidence intervals (Figure 5.15). This surface
illustrates large uncertainties associated with error predictions in Ontario and
lesser uncertainties in Michigan. The tightest confidence intervals are near NGS
benchmark locations, where I have the best estimates of DEM error. As
described in Chapter 4, relatively few benchmarks were available to assess
elevations in the Ontario region, but of those that were, many revealed large
errors. In sum, average DEM error magnitudes in the Michigan subsets tend to
be smaller than those in the Ontario subset; more is known about the spatial
structure of DEM errors in the Michigan subsets than is known for the Ontario

subset; and, consequently, error predictions in the Michigan subsets are made

231

with greater certainty than those made at unsampled locations in the Ontario

subset.

  

 

95% confidence interval
about the prediction (m)

I 12.1 to 15.2
I 9.1 to 12.0
6.1 to 9.0
E} 3.1 to 6.0
[:l 1.8 to 3.0

     
  

for

I
W
l
l

 

 

 

 

 

 

 

Figure 5.15: Uncertainty in the surface of predicted DEM errors. Darker tones
are associated with larger confidence intervals and hence greater uncertainties.
Areas shown in white were masked from analysis to facilitate computation.

Running the spatial model

Monte Carlo simulation is a computer-intensive framework that is useful
for revealing contributions of random input data errors, differences among
uncertainties across a geographic region of interest (Burrough and McDonnell,
1998) and uncertainties that lurk in spatial model results. In essence, a typical
simulation consists of evaluating a spatial model many times, each time using
input data that have been modified randomly via a model that expresses an error

distribution or makes assumptions about error behavior.

232

I ran my spatial model 100 times for each lake phase (i.e., Main, Ardtrea,
Upper Orillia, and Lower Orillia). Specifically, I used the appropriate model of
differentially-upwarped water plane elevations and one of a hundred
realizations of ground surface elevations (i.e., the DEM) as inputs. Each DEM
realization consisted of original DEM elevation values that were perturbed by a
model of random and spatially-structured errors, which was made conditional to
errors measured at NGS benchmark locations.

DEM realizations were generated using a five-step procedure. As
described above, the spatial structures among subsets of DEM errors were
modeled by fitting three variogram models to three empirical variograms.
Second, I used errors measured at NGS benchmark locations, the appropriate
variogram model and ordinary kriging to predict error distributions at every cell
location within each subset. Third, I employed sequential Gaussian simulation
(565) to draw randomly error values from each predicted distribution at every
cell location within a subset. Fourth, I appended the three regional error surfaces
to create a composite realization of DEM error for the entire study area. I
included maps of two of one hundred error simulations (Figure 5.16) below.
And fifth, I subtracted the composite error surface from the original DEM,
thereby generating an alternate possible realization of the original DEM. I
generated one hundred such realizations for the study area. Alternate DEM
realizations are visually indistinguishable from the original DEM, so I have not

included figures to show them.

233

Predicted error (m)

I 16.1 to 39
E] 3.1 to 16.0
|:| -3.0 to 3.0
-16.0 to -3.1
I -39 to -16.1

Not predicted
Set to zero

 

 

 

 

 

 

 

 

Predicted error (m)

I 16.1 to 39
[:1 3.1 to 16.0
|:] -3.0 to 3.0
-16.0 to -3.1
I -39 to -16.1

Not predicted
Set to zero

 

 

 

 

 

 

 

 

b) Results of error simulation #87.

Figure 5.16: Composite surfaces of DEM errors. Cells shown in gray were
masked from analysis to facilitate computation, but later set to zero. The image
in this dissertation is presented in color.

Shorelines were interpolated, in effect, by comparing spatially-coincident
elevation values in each DEM realization to those along a modeled water plane.
Grid cell locations with DEM elevations greater than water plane elevations were
classified as above water (1); the balance was classified as not above water (0).
Boundaries between cells coded with 1’s and those coded with 0’s represent
paleoshorelines - the former land and water interface. Each set of 100 binary
results was then summed using grid algebra to produce a final grid; one final
grid for each lake phase. Each final grid contains cells with values ranging
between 0 and 100 and each value indicates the number of times a cell was
classified as above water. For example, a cell with a value of 0 indicates a location
that was predicted to be above water zero times, or zero percent of the time,
despite errors in the DEM. A cell with a 100 value indicates a location that was
predicted to be above water 100 times, or 100 percent of the time, despite errors in
the DEM. Cells with intermediate values express uncertainty and thus possible
membership in both the above water and not above water classes; values near 50
express the greatest uncertainty regarding whether or not a location was above
or not above the ancient water plane. Such cells hold results of the spatial model
have been rendered uncertain by errors in input data. The set of four final grids

are presented and discussed in Chapter 6.

235

Summary

In this chapter I described the components of a spatial model used for
reconstructing five glacial Lake Algonquin water planes and interpolating each
respective set of shorelines. Initial reconstructions of differentially-upwarped
water planes were supported by paleoshoreline position data and parameters
that describe rates of uplift were estimated via ordinary or generalized least
squares. Water planes were reconstructed ultimately via universal kriging,
which yielded both a surface of predicted elevations and an estimate of
uncertainty at each location within the study area.

The Main, Ardtrea, Upper Orillia, and Lower Orillia water plane surfaces
generated during this work (Figures 5.6a, 5.8a, 5.10a, and 5.12a) look similar to
the water plane surfaces derived from paleoshoreline data by Schaetzl et al.
(2002). The water plane models reported in this work, however, are superior to
the water plane models presented by Schaetzl et al. (2002) in five important
ways. First, each of my models is supported by more paleoshoreline data that
cover larger geographic extents. Recall, the geographic distribution of the
original glacial Lake Algonquin dataset was oriented roughly along the expected
trend and no normal to it. New paleoshoreline data were collected along an axis
normal to expected uplift trends to better capture these trends. Second, each of
my models incorporates data taken from Ontario, where Lake Algonquin
shorelines have long been recognized. Accordingly, bluff sites that were

rnisclassified by Schaetzl et al. (2002) and Farrand and Drexler (1985) were

236

 

reclassified (Chapter 3) and have been integrated into the findings reported by
Sly and Lewis (1969), Cowan (1985), and Karrow (1987). Third, I used a reduced
second-order trend model to capture the uplift trend; all model parameters were
found to be statistically significant. Schaetzl et al. (2002) used a full second-order
model that retained a statistically insignificant term, which renders their model
as less meaningful. Fourth, my geostatistical rebound models take into account
both the broad regional uplift trend and localized deviations from that trend that
likely result from differences among site conditions; Schaetzl et al. (2002) focused
on the trend only. And fifth, before geostatistical analysis, I rescaled all location
coordinate values from the meter to the kilometer unit of measure, and
translated the planar coordinate system origin from a location outside the State
of Michigan to Traverse City, Michigan to reduce coordinate magnitudes. This
coordinate transformation mitigated rounding errors created during trend
surface analysis and by computer word overflows (Burrough and McDonnell,
1998) - especially when coordinate values were raised to powers greater than
one for use in second- or higher-order trend models. The full second-order trend
surface models reported by Schaetzl et al. (2002) were surely influenced by such
rounding errors and, therefore, the parameter coefficients obtained from them
cannot be considered accurate. Also, my trend model coefficients express rates
of uplift in m/ km, which is more user-friendly than the rates they reported in
m/ m. In these five ways, the water plane models reported in this work are

superior to the water plane models presented by Schaetzl et al. (2002).

237

The Lake Algonquin water plane surfaces generated during this work
(Figures 5.6a, 5.8a, 5.10a, and 5.12a) also look similar to postglacial rebound
surfaces derived from lake gauge data (e.g., Coordinating Committee, 1977, 2001;
Tushingham, 1992; Mainville and Craymer, 2005), and others derived from a
geophysical model (e.g., Tushingham and Peltier, 1991). Figure 5.17 shows a
surface of uplift rates derived by Tushingham and Peltier (1991) and Figure 5.18
shows the latest surface of uplift rates created by Mainville and Craymer (2005).
Like these surfaces, Lake Algonquin water planes are continuous, smooth, and
show a general pattern of uplift that tends to increase in Michigan from the

southwest to the northeast and towards the former centers of ice loading.

  
 
  
  
  
 

   
    
       
 
   

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Figure 5.17: Contemporary uplift rates (cm/ century) derived from the ICE-3G
geophysical model (Tushingham and Peltier, 1991). Figure adapted from
Tushingham (1992: 445).

238

 

Figure 5.18: Contemporary uplift rates (cm/ century) derived from historical lake
gauge data. Figure adapted from Mainville and Craymer (2005: 1077).

With respect to the study area, the water plane surfaces built during this
work share more similarities with the uplift surface built by Mainville and
Craymer (2005) than with the uplift surface built by Tushingham and Peltier
(1991). For example, as elevation contours pass through northern Michigan from
east to west, they tend to bend more toward the west and less toward the north -
just like the isobases depicted in Mainville and Craymer’s (2005) map. The
isobase pattern in Figure 5.18 is supported by 55 gauge stations and was derived
via a least-squares adjustment method; it depicts a regional uplift pattern and
what appear to be localized deviations from that pattern - similar to the regional

and local patterns depicted in my Main and Upper Orillia surfaces (Figures 5.6

239

and 5.10, respectively). By comparison, the ICE-3G surface (Figure 5.17) is a
much smoother surface, probably because it does not rely on a least-squares
model and it is supported by a global dataset with fewer data points in the
region of interest. The apparent degrees of similarity between contours on the
Lake Algonquin water planes and isobases on Mainville and Craymer’s (2005)
map suggests my surfaces are reasonable and, importantly, that the pattern of
isostatic recovery has not changed much during that last 11,000 years.
Information about elevation errors at NGS benchmark locations was used
to condition assumptions about error in a DEM and, via ordinary kriging and
Monte Carlo simulation techniques, generate alternate possible realizations of
contemporary ground surface elevations. Finally, results of the two components
(a predicted water plane and a DEM realization) were used as inputs to the
spatial model. Inputs were combined to allow locations within the area of
interest to be characterized as: above water; not above water; or, possibly either (i.e.,
the classification was uncertain). In sum, ancient landscapes associated with the
Main, Ardtrea, Upper Orillia, and Lower Orillia phases of glacial Lake
Algonquin have been digitally reconstructed. Their shorelines occur within the

bands of uncertainty that exist between above water and not above water areas.

240

CHAPTER 6: MAPPING THE RESULTS

Introduction

This chapter summarizes results of the four shoreline interpolation
models described in Chapter 5 and presents two maps for each modeled lake
phase. The first indicates where ancient shorelines probably occurred. Shorelines
are not represented by lines drawn with a constant width; rather as bands of
varying widths. I refer to these bands as bands of uncertainty because the exact
location of the former land and water interface is indeterminate given errors and
uncertainties in the datasets I employed. The second map offers a similar view of
the landscape as well as a fog that, ironically, reveals the spatial pattern of
uncertainty associated with the reconstructed water plane. Revealing two kinds
of uncertainty in maps of glacial Lake Algonquin shorelines, these associated
with errors in the DEM and others associated with the spatial pattern of
imprecision along the reconstructed water plane, provides the map reader with
information that he or she can use to assess the quality of these results in terms of
his or her intended use. I believe these maps are useful for locating shorelines

and targeting areas that require additional inquiry.

Summary of results obtained from the spatial model
I used a spatial model to reclassify cells in a digital elevation model to
reveal the extents of four ancient lake phases (see Chapter 5, this volume).

Output cells contain values ranging from O to 100; each value indicates the

241

number of times a cell was classified as above water. For example, a cell with a
value of 0 was predicted, despite the range of possible errors in the DEM at that
location, to be above water zero times, or zero percent of the time. A cell with a
100 value was predicted, despite the range of possible errors in the DEM at that
location, to be above water 100 times, or 100 percent of the time. Cells with
intermediate values express uncertain memberships in the above water and not
above water classes; values near 50 express the greatest uncertainty regarding
whether or not a location was above the water plane because input data errors
have upset the classification process.

The number of uncertain cells that separate above water areas from not
above water areas varies with location. The width of each band of uncertainty is
generally sensitive to two factors: the vertical distance between a ground surface
elevation and the expected water plane elevation; and the beach slope where the
ground surface and water plane intersect. The precision with which the vertical
distance between an indeterminate ground surface elevation and an expected
water plane elevation can be measured, however, is sensitive to the horizontal
distance between a DEM grid cell and the nearest ground control point used to
condition the DEM error simulation model.

I used a set of errors measured at 529 ground control points to condition a
computer simulation that generated 100 alternate possible realizations of DEM
error and, subsequently, 100 alternate possible realizations of the original DEM.

The spatial structure of error was modeled on a regional basis by one of three

242

variogram models, each with a nugget parameter that specified the small amount
of noisy variance expected at control point locations, a sill parameter that
specified the larger amount of variance expected at locations far from control
points, and other parameters that specified how covariance increases with
distance. According to these models, the precision of DEM elevations tends to
decrease with distance from control points because information is known about
the errors that occur at control points and less is known about errors that occur at
locations far from control points. The precision of measured ground elevations,
in turn, directly influences the precision of vertical distances measured between
expected DEM elevations and glacial Lake Algonquin water planes. As a water
plane approaches the DEM it enters the tails of larger elevation distributions,
which are generally situated far from control point locations and subjected to
larger error distributions, sooner than it enters the tails of smaller elevation
distributions, which are generally situated near control points and subjected to
smaller error distributions. Consequently, DEM cell locations are typically
classified with greater certainty as the horizontal distance between DEM grid
cells and control points decreased.

The second factor, the beach slope at the expected shoreline, is related to
shorezone morphology. As beach slope decreases, the surf zone widens and the
width of the band of uncertainty tends to increase. For example, if the slope
gradient is 90 degrees (e.g., waters lapping against a vertical cliff or wall), then

the ground surface will, setting erosion aside, yield little landward movement of

243

the shoreline as water level changes. Many relict wave-cut bluffs have long and
steep slopes that constrained the landward movement of water, which is one
reason they are good indicators of former shorelines. As beach slope decreases
toward 0 degrees (e. g., waters swashing over a flat beach), however, variations in
water level (in this case, uncertainty about ground surface elevation) will force
greater horizontal shoreline movements and, hence, greater uncertainty
regarding the exact location of the shoreline along the horizontal plane. Low-
gradient beaches do not confine variations in water level, but allow the water
surface to extend landward or retreat lakeward with changes in water level (or,
in this case, with uncertainty about ground surface elevations).

The range of possible interactions among beach slope and data precision
might become clearer with two more examples. First, consider a neighborhood
of four DEM grid cells that represents the edge of a morainic upland and is
situated near a benchmark. Two cells have elevations that tower above the
expected water plane and the others have elevations that rest far below, thus
implying a steep slope among them. Moreover, the magnitude of error at each
cell is estimated with tight precision because the benchmark is proximate and the
variogram model provides good information about the amount of error in the
neighborhood. The spatial model can classify these cells consistently over 100
runs because the vertical distance between each cell and the water plane can also
be estimated with tight precision. Ultimately, the area of uncertainty is mapped

as a very narrow band.

244

Consider another neighborhood of four DEM grid cells that represent an
area situated in a wetland and far from any benchmark; all four cells have similar
elevations that are near the water plane. The magnitude of error at each cell can
be estimated with loose precision only because the nearest benchmark is situated
beyond the range of observed spatial structure and the variogram model can
provide no helpful information other than the variance of errors. Consequently,
the spatial model is unable to classify cells in this neighborhood consistently over
100 runs given the wide range of simulated elevations at each cell. Ultimately,
the entire neighborhood is mapped within a broad band of uncertainty.

Using these two examples as ”straw men,” it is easy to imagine spatial
patterns of beach slope (from flat to steep) and data precision (from tight to
loose) and how they might interact across space and differentially perturb the
classification process from one grid cell to a next.

To put these uncertainties into some perspective, the amount of area
(within the study area) that was submerged by each lake phase was determined
under three different scenarios. Using the classification results described above,
the liberal scenario involved summing the areas of cells that were not classified
as above water at least ninety percent of the time, which should yield a relatively
large estimate of submerged area. The moderate scenario involved summing the
areas of cells that were not classified as above water at least fifty percent of the
time. The conservative scenario involved summing the areas of cells that were

not classified as above water at least ten percent of the time, which should yield

245

the smallest or most conservative estimate of submerged area. Percentages were
calculated to express the relative amount of area in the study area that was under
water during each lake phase. Today, 14,446 km2 (31 %) of the study area (46,468
kmz) is covered by contemporary Great Lakes water. Table 6.1 lists these results.
As expected, the smallest submerged areas are associated with the lowest water
plane (Lower Orillia). The largest submerged areas are associated with the
highest water plane (Main phase), which covered nearly twice as much area as
do the contemporary Great Lakes. Submerged area values increased by 300 to
500 km2 as the selection criterion was relaxed and more cells with less certain
classifications were counted. These results show that these area calculations

were sensitive to the uncertainties that propagated through the spatial model.

Table 6.1: Estimates of total land area under water during each lake phase.
Percentages of contemporary land area under water are indicated in parentheses.

Estimates of area under each water plane

 

 

Conservative Moderate Liberal

Lake phase km2 (%) km2 (%) km2 (%)
Main 27,957 (60) 28,556 (61) 29,146 (63)
Ardtrea . 27,012 (58) 27,662 (60) 28,300 (61)
Upper Orillia 25,775 (55) 26,357 (57) 27,119 (58)
Lower Orillia 24,284 (52) 24,785 (53) 25,420 (55L
Contemporary 14,466 (31) 14,466 (31) 14,466 (31)

 

Maps of glacial Lake Algonquin shorelines

To prepare each final grid for display, I reclassified grid cells into one of

three map categories. Cells predicted to be above water fewer than 10 percent of

246

the time were reclassified as probably below water and symbolized with a light
gray tone. Cells predicted to be above water more than 90 percent of the time
were reclassified as probably above water and symbolized with a medium gray
tone. Cells with intermediate values were reclassified as uncertain (i.e.,
indeterminate) and highlighted with black. Grid cells associated with the
contemporary Great Lakes are symbolized with white.

I symbolized map categories using a four-tone grayscale and established a
visual hierarchy to draw the map reader’s attention to the shorelines. I use black
to emphasize shoreline locations and white to serve as background and provide
contrast. I selected the balance of gray tones to also contrast well with black and
allocated them in a way that establishes land as figure and water as ground. For
example, I use a medium gray tone to represent probably above water areas. When
mapped, these homogenous-looking uplands attain figure because they are
distinguishable and surrounded by shorelines (Robinson et al., 1995). Yet, the
shapes of land areas during glacial Lake Algonquin times were much different
than they are today; many readers might not recognize the region, or specific
places within the region. So, I added contemporary county boundaries to
provide a frame of reference. I used a light gray fill to ensure the political units
were distinguishable from all other categories, but less distinguishable from the
background and more so from objects in the foreground. Figure 6.1, 6.2, 6.3 and
6.4 illustrate the Main, Ardtrea, Upper Orillia, and Lower Orillia shorelines,

respectively.

247

 

   

Sh Jose h
. P

 

Munuscong . .31lsland
. ‘1‘, q}, Islands .3
./ Mackinac Island Cockbiiwf
" Island
L a k e

llBeaver

     

3, Island ' r032

 

 

Figure 6.1: Predicted shorelines of the Main phase of glacial Lake Algonquin in
the study area. Shorelines are represented as blackened areas; greater widths
imply greater uncertainty about shoreline location.

248

 

 

. é‘rJoseph RTE»

        

  
  
 

, Munuscong Island
Q Islands

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Figure 6.2: Predicted shorelines of the Ardtrea phase of glacial Lake Algonquin
in the study area. Shorelines are represented as blackened areas; greater widths
imply greater uncertainty about shoreline location.

249

 

 

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Munuscong ‘ 33318.3“

   

   
    

Islands :3" .. .3..-
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Figure 6.3: Predicted shorelines of the Upper Orillia phase of glacial Lake
Algonquin in the study area. Shorelines are represented as blackened areas;
greater widths imply greater uncertainty about shoreline location.

250

 

 
  

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Figure 6.4: Predicted shorelines of the Lower Orillia phase of glacial Lake
Algonquin in the study area. Shorelines are represented as blackened areas;
greater widths imply greater uncertainty about shoreline location.

251

A word of caution is required. The shorelines mapped above do not
necessarily represent actual shorelines. The land surface has undoubtedly been
modified over the 10,400-year period since Lake Algonquin ended. Evidence of
higher shorelines has likely been destroyed at many locations by wave action at
the perimeter of later and lower water planes. Rivers and streams have
deepened channels and moved materials form one location to another.
Therefore, the best that can be said about these maps is that they depict what the
landscape would look like today if contemporary lake waters were to somehow
rise and reoccupy the abandoned ancient water planes.

Figures 6.1, 6.2, 6.3 and 6.4 are remarkable in several respects. First, they
represent the first known attempt to map the entire ” Upper Group” of glacial
Lake Algonquin beaches in this region. Second, these figures show locations that
emerged as water levels fell, especially in the Upper Peninsula and along the
archipelago now stranded in the Lower Peninsula. For example, several spits
reported by Krist and Schaetzl (2001) are conspicuous in maps of the Ardtrea and
Upper Orillia phases. Third, this series suggests waters in the Michigan and
Huron basins remained hydrologically connected via the Indian River lowland.
And fourth, all four maps exhibit striking similarities, particularly in southern
portions of the region where water plane models tend to converge.

Similarities among Figures 6.1, 6.2, 6.3, and 6.4 are greatest in areas north
of Traverse City and south of Alpena, where water planes tend toward

convergence. Karrow reported the Main Algonquin shoreline between

252

Kincardine and Port Elgin, Ontario, along the eastern shore of Lake Huron, ”has
been entirely removed by later shore erosion by lower water levels after the
Main Algonquin level” (Karrow, 1987: 161). I believe the same kind of bluff
removal processes have occurred north of Traverse City and south of Alpena.
Consequently, I also believe it makes better sense to attribute observable
shorelines in these areas to the last phase to act upon them; not the first or the
highest. Therefore, I can agree with Larsen’s claims that Main and Ardtrea
shorelines of eastern Lake Huron predate the highest stranded shorelines in
northern Lake Michigan, and the apparent ”Main” shoreline of Lake Michigan

”may correlate with the Orillia shoreline of Ontario” (Larsen, 1987: 21).

The Main phase

The Main phase was the highest and longest-lasting phase of the glacial
Lake Algonquin sequence. I used a sample of 59 features to reconstruct the Main
water plane; all but one are located north of an imaginary line connecting Alpena
and Charlevoix, Michigan. Contours along the uplifted water plane (Figure 5.6a)
reveal a deformation pattern of uplift and curvature that is similar to others
patterns mapped by Goldthwait (1910), Schaetzl et a1. (2002), and Mainville and
Craymer (2005). Clarke et al. (1994) built numerical models of glacio-isostatic
recovery to estimate the thickness of the ice sheet in this region. The pattern of

deformation shown in Figure 5.6 is more closely aligned with the pattern of

253

deformation predicted via their thin ice sheet model than with the pattern
predicted via their thick ice sheet model.

Figure 6.1 highlights areas over which shorelines probably occurred.
Narrow bands of uncertainty (~100 to 200 m) are often associated with large
bluffs, steep-gradient shorezones, and an ample supply of nearby ground control
points. For example, one narrow band is situated south of Alpena and along the
base of ”the old lake bluff cut sharply into high morainic ground. For 10 miles
the bluff is high and bold” (Leverett and Taylor, 1915: 420). US Highway 23
follows the base of this high bluff and ten NGS benchmarks situated along this
stretch of road were used to condition simulations of the DEM. The combination
of steep ground slope and good ground control enabled the spatial model to
classify cells in the region consistently.

As expected, shorelines mapped as relatively wide bands of uncertainty
(~ 1 to 2 km) are often situated in what were low-gradient shorezones and / or
areas that contain few ground control points. For example, the area on the map
associated with the ” great sand plain west of Alpena” (Leverett and Taylor,
1915:421) is peppered with uncertainty, which implies the classification process
was sensitive to errors in the digital elevation model and the relatively flat
topography of the region. Only one NGS benchmark ((210289) provides ground
control for much of this region. And, Leverett and Taylor described the area as
”a wide plain of sandy gravel” that runs ”for considerable distances”, and

claimed the exact location of the shoreline ”is difficult to determine” (Leverett

254

and Taylor, 1915: 420). My fieldwork and these results support that claim.
Nevertheless, these results offer what previous research has not - a probabilistic
surface that indicates, based on the data and information available, where
shorelines likely occur and where evidence of shorelines might be found.

I am always amazed by the extent of land in the Upper Peninsula that was
once submerged by glacial Lake Algonquin waters. The Munuscong Islands and
several morainic features were all that stood above the highest lake surface.
Shorelines around the Munuscong Island complex are mapped as narrow bands
of uncertainty. Much of the area northwest of the Munuscong Islands occurs at
elevations at or near the water surface, and it seems the classification process was
sensitive to errors in the digital elevation model and the relatively flat
topography of the region. Many shorelines here are mapped as wide bands of
uncertainty.

The Ontario portion of the digital elevation model suffers the largest range
of error compared to the other portions that represent the Upper and Lower
Peninsulas of Michigan. It also contains over-represented elevations that were
likely derived from 50-foot contour lines printed on topographic maps (Chapter
4). A consequence of including oversampled contour elevations in a DEM is the
fabrication of flat areas or benches in the digital model that do not exist on the
real landscape. In the context of the spatial model employed in this work,
artificial benches that have surface elevations close to predicted water plane

elevations can negatively impact spatial model performance because such

255

benches would have introduced greater uncertainties into the final results. For
example, a cell that holds a contour elevation that over represents actual
elevation will tend to be classified as above water more often than it should.
Conversely, a cell that holds a contour elevation that under represents actual
elevation will tend to be classified as above water less often than it should.
Paradoxically, cells with contour elevations that are over classified as above water
will tend to be situated lakeward (down slope) of the contour line, and cells with
contour elevations that are under classified as above water will tend to be situated
landward (up slope) of the contour line! Nevertheless, it seems that the
substantial relief that exists between Ontario’s high bedrock uplands and low
lake plains was more than enough to overcome both the artificial benching
problem and the propagation of uncertainty about DEM error through the spatial
model, for, surprisingly, most shorelines in the Ontario region are mapped as
relatively narrow bands of uncertainty. The Ontario portion of the study area,
therefore, contains many bedrock hills that might have existed as islands in Main
Lake Algonquin. I use the word ”might” because Karrow (1987) claims the ice
sheet uncovered the area for only a brief time toward the end of the Lake

Algonquin sequence.

The Ardtrea phase
Deane described the Ardtrea phase as a ”brief period of quiescence”,

because the character of Ardtrea features in his study area was relatively weak

256

and indicated relatively little wave action. He also claimed the ” [Main]
Algonquin and Ardtrea beaches tend to converge toward the south" (Deane,
1950: 73). I used relative differences in character and elevation to distinguish 41
stranded Ardtrea features from the many higher features of Main; all but four are
located north of an imaginary line connecting Alpena and Charlevoix, Michigan.
Contours along the uplifted water plane (Figure 5.8a) show a deformation
pattern of uplift and curvature that is similar to the pattern exhibited in Figure
5.6a. Of all the water plane models built in this work, the Ardtrea model
provides the best statistical fit to data.

Figure 6.2 highlights areas over which shorelines probably occurred.
Again, narrow bands of uncertainty are often associated with large bluffs, steep-
gradient shorezones, and an ample supply of nearby ground control points.
Shorelines mapped as relatively wide bands of uncertainty are often situated in
what were once low-gradient shorezones and contain few ground control points.

Spurr and Zumberge (1956) identified relict shoreline features in
Cheboygan and Emmet Counties, Michigan, that occur 5 to 8 meters below Main
Algonquin. The authors interpreted them as evidence of a pre-Lake Algonquin
lake. Earlier and later work, however, (Leverett and Taylor, 1915, Krist and
Schaetzl, 2001, respectively) characterized the same features as belonging to spits
formed in glacial Lake Algonquin. I accepted the later interpretation and

correlated several bluffs in the area with the Ardtrea phase, and lower ones with

257

the Upper Orillia. Figure 6.2 reveals the footprints of several large features that
clearly look like spits that formed at, or just beneath the Ardtrea surface.

The footprint of Leverett and Taylor’s ”morainic tract" (Leverett and
Taylor, 1915:425) on Beaver Island is visible. And, as expected, only the
northern, higher portion was consistently classified as above water.

Distances between successive water plane elevations are greatest in the
north, which explains why so much land area in the Upper Peninsula emerged
between the Main and Ardtrea phases and so little emerged in more southerly
locations. For example, the Munuscong Islands coalesced into one large island
while a fourth and smaller island emerged to the east. Although many Ardtrea
shorelines are depicted as relatively wide bands of uncertainty in the Upper

Peninsula (~2 to 4 km), they are narrower than those associated with the Main

phase (~3 to 6 km).

The Upper Orillia phase

Deane characterized evidence of the Upper Orillia phase as the ”most
conspicuous between the Wyebridge and the [Main - au thor’s inclusion]
Algonquin” (Deane, 1950: 74). Yet, to my knowledge, the Upper Orillia phase
has never been mapped. I used a sample of 33 features to reconstruct the Upper
Orillia water plane, which includes a massive bluff at Cockburn Island, Ontario.
The Upper Orillia water plane is supported by fewer data than supports the

Main or Ardtrea water planes, and Upper Orillia data span a greater extent than

258

both. Perhaps that is why, of the three, the Upper Orillia water plane model is
the noisiest, least precise, and subject to the greatest statistical uncertainties.
Nevertheless, contours along the uplifted water plane (Figure 5.10a) show a
deformation pattern of uplift and curvature that is similar to the patterns
revealed in the Main and Ardtrea water planes and similar to the patterns
expressed in previous research. Figure 6.3 highlights areas over which Upper
Orillia shorelines probably occurred given all the information that is available.

Figure 6.3 shows many interesting features. For example, the footprints of
the Riggsville Island, Owens Island, and the Ocqueoc spits (Krist and Schaetzl,
2001) are revealed quite clearly. Proto-Beaver, Cockburn and Mackinac Islands
are conspicuous. And, many of the largest islands in the Lower Peninsula
archipelago, via the bands of uncertainty that connect them, show signs of
emergence and coalescence.

The embayment that holds contemporary Walloon Lake (Lower Peninsula
near Charlevoix) is mapped as a band of uncertainty during Upper Orillia times,
which suggests the ancient water plane is close to the contemporary water
surface. From these results, it is reasonable to hypothesize that waters in the
Walloon Lake embayment were last connected to glacial Lake Algonquin during
the Upper Orillia phase. Today, the surface of Walloon Lake rests (209 m) higher
than the surface of Lake Michigan (177 m).

The most interesting aspect of the predicted Upper Orillia water plane

model is that it intersects the predicted Ardtrea plane at the mouth of the Au

259

Sable River; the two converge at 196.3 m. Convergence suggests transgression by
the later lake phase. The line of intersection, or axis, should be connected to a
controlling outlet. According to Larsen (1987: 7), ”North of the axis the
shorelines descend from the oldest to youngest, but to the south the evidence is
submerged with the oldest shoreline at the bottom of the sequence.” The Upper

Orillia plane is supported by data at this location, but the Ardtrea plane is not.

The Lower Orillia phase

I had difficulty identifying features related to the Lower Orillia phase, just
as Cowan (1985) did in his work at Sault Ste. Marie, Ontario, and Deane (1950) at
Lake Simcoe, Ontario. The features I used to model the Lower Orillia water
plane are few (n=16) and far between; they share little commonality other than
having elevations too low to be correlated with the Upper Orillia and too high to
be correlated with one of the ”Lower Group” beaches. Contours along the
reconstructed water plane (Figure 5.12a) show a deformation pattern of uplift
and curvature that is unlike the patterns exhibited in Figures 5.6a, 5.8a, or 5.10a;
the degree of warping is severe and the pattern of deformation does not resemble
any previously-mapped pattern, particularly in the Lower Peninsula. Therefore,
I believe these results are merely speculative, perhaps provisional in the Upper
Peninsula where most of the data are located, even though the Lower Orillia

water plane model is fit reasonably well to data that support it.

260

Figure 6.4 highlights areas over which shorelines probably occurred given
available data. By comparison with the others, it reveals the continued
emergence, expansion, and coalescence of upland areas in the Upper Peninsula.
And, it reveals areas in the Lower Peninsula, particularly along the archipelago

and the mouth of the Au Sable River, where new lands emerged.

Maps of glacial Lake Algonquin shorelines that reveal uncertainty

Figures 6.1, 6.2, 6.3, and 6.4 reveal the extents of four former lake phases in
the area of interest. Shorelines widths indicate the amount of uncertainty
generated by DEM errors that propagated through the spatial model. What
Figures 6.1, 6.2, 6.3, and 6.4 do not reveal, however, are uncertainties about the
water plane models that were used to derive these results.

Figures 6.1, 6.2, 6.3, and 6.4 were built using water plane surfaces that
were fit statistically through point samples via universal kriging. These models
respect the points that support them, but do not always predict well in locations
removed from data. In addition to prediction surfaces, the universal kriging
tools I employed allowed me to generate surfaces of mean square prediction
errors, sometimes called kriging variances. Kriging variances provide the basis
for deriving confidence intervals at locations where elevations values were
predicted (Bailey and Gatrell, 1995). Using a specified level of confidence, 95% is
typical, a single confidence interval can indicate the precision with which a single

value was predicted, or stated another way, uncertainty about the prediction.

261

Greater uncertainty is associated with lesser precision, and vice versa. When
confidence intervals are mapped over space they can reveal the spatial pattern of
uncertainty in the prediction model.

A common approach to represent uncertainty in static maps is to start
with Bertin’s (1967/1983) visual variables and manipulate them using traditional
cartographic techniques (MacEachren, 2005). MacEachren suggests using a gray
fog that hovers over the mapped area and ”obscures the map theme in
proportion to the uncertainty in data about the theme” (MacEachren, 1995: 276).
He prefers a gray fog because, according to him, grayness is associated with
uncertainty: ”more ’ gray’ equals more uncertain” (MacEachren, 1995: 441). Yet,
there is little agreement in the literature about the best method of representing
uncertainty, which visual variables are the best to manipulate, or how visual
variables should be used. Hengl (2003), for example, manipulated color
saturation to indicate relative differences in uncertainty. In his work, more white
equals more uncertain; more hue equals more certain. Alternatively, Leitner and
Buttenfield (2000) found variations in color value were most effective in
depicting variation in uncertainty; lighter values represent greater certainty and
darker values represent greater uncertainty.

I employed MacEachren’s cartographic concepts of fog and transparency
(MacEachren, 1992, 1995, 2005) to reveal the spatial pattern of uncertainty in each
water plane model, but chose a black fog instead of a grey one. The fog was

made completely transparent at locations associated with relatively small

262

confidence intervals (less than 3 m with 95% confidence), thereby revealing
completely the underlying data. I reduced transparency to 33% at locations
where the size of the confidence interval about the predicted water plane
elevation exceeded 3 meters but was less than 6 meters. I reduced transparency
to 67% at locations where the size of the confidence interval about the predicted
water plane elevation exceeded 6 meters but was less than 7 meters. And, at
every location where the water plane could not be predicted with better than 9
meters of precision (95% confidence), transparency was reduced to 0% to obscure
the underlying results completely. In general, the opacity of the black fog of
uncertainty increases with distance from sampled bluff locations at a rate
determined by the geometry of sampled bluffs and covariance structure specified
by the supporting variogram model.

Superposing a layer of black fog over areas already mapped in tones of
gray produced unwanted visual effects. Specifically, areas mapped as probably
below water and symbolized with a light gray tone were rendered darker at
locations where the water plane elevation was not predicted precisely; these
areas could not be distinguished easily from others mapped as probably above
water with tight precision. Ultimately, I abandoned my original grayscale and
employed two hues: brown to represent locations above the water plane and
blue to represent locations below water. Superposing a layer of black fog over

areas mapped with different color hues achieved the desired visual effect.

263

Figures 6.5, 6.6, 6.7, and 6.8 reveal the extents of glacial Lake Algonquin
lake phases. Shorelines are again represented as black bands of varying width
over which ancient shorelines probably occurred. Wide band widths imply
greater uncertainty regarding the former location of the land and water interface;
uncertainty that results from DEM errors that propagated through the spatial
model. In addition, uncertainty in the water plane surface model is depicted as a
black fog of apparent varying density. Areas with denser fogs imply greater
uncertainties regarding the water plane predictions and typically occur in areas

far from sampled locations.

Composite maps of Main Lake Algonquin and the Upper Group

I prepared one final map, without any fog, to represent all four sets of
shorelines. I selected and mapped all areas that were predicted by my spatial
model to be above water 90 times out of 100 runs. Figure 6.9 shows locations
that stood above Main Lake Algonquin waters (dark gray), and locations that
emerged during the Upper Group sequence. Locations below all water planes
and above the contemporary land surface are symbolized with a light gray tone.
Large areas in the Upper Peninsula and small areas in the Lower Peninsula, the
sand plain near Alpena for example, exhibit the greatest change over time. I then
created Figures 6.10, 6.11, 6.12, 6.13, 6.14, and 6.15 to focus attention on selected
areas where field campaigns were conducted (Chapter 3). These figures can be

referenced using the index map shown in Figure 3.4.

264

 

 

 
  
    
 
          

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in the water plane.

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20 10 0 20
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Figure 6.5: The Main phase of glacial Lake Algonquin. Darker tones indicated
greater uncertainties about the predicted water plane. The image in this
dissertation is presented in color.

265

 

  
 

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036912

20 10 o 20 9
Uncertainty about the waterplane (m) EEEEEEEIE kilometers

 

Figure 6.6: The Ardtrea phase of glacial Lake Algonquin. Darker tones indicated
greater uncertainties about the predicted water plane. The image in this
dissertation is presented in color.

266

    
 
  
   

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Figure 6. 7: The Upper Orillia phase of glacial Lake Algonquin. Darker tones
indicated greater uncertainties about the predicted water plane. The Image in
this dissertation is presented in color.

267

 

 
   
 

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Uncertainty about the waterplane (m) HERE kilometers

 

Figure 6.8: The Lower Orillia phase of glacial Lake Algonquin. Darker tones
indicated greater uncertainties about the predicted water plane. The image in
this dissertation is presented in color.

268

 

 
   

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Figure 6.9: The Main (dark gray), Ardtrea (pink), Upper Orillia (purple), and
Lower Orillia (green) phases of glacial Lake Algonquin. The image in this
dissertation is presented in color.

269

Proto-Cockburn Island began as an islet less than 1 km2 in size (Figure
6.10). Main and Upper Group shorelines are closely spaced here and indicate the
island grew only slightly larger during the Main and Upper Group phases.
Relict shoreline features on Cockburn Island are isolated and situated well out
from the mainland. These features provided important support to water plane

reconstructions in this portion of the study area.

 

 

Figure 6.10: Areas on Cockburn Island that were predicted to be above glacial
Lake Algonquin water levels. The extent of this figure corresponds with the
extent of Figure 3.5. The image in this dissertation is in color.

270

Figure 6.11 shows the Munuscong Islands region. Four small islands
appear to have emerged and coalesced through the Main and Upper Group
sequence. Also, two new islands emerged to the east as lake levels fell. The
irregular outline of the islands that Taylor (1895) first described is clear to see as

is the ”sweep of low ground” between the islands and Hessel that ”has the

appearance of a recently deserted lake bottom” (Taylor, 1985: 26).

 

 

 

 

 

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Figure 6.11: Areas in the Munuscong Island region that were predicted to be
above glacial Lake Algonquin water levels. The extent of this figure corresponds
with the extent of Figure 3.11. The image in this dissertation is in color.

271

Figure 6.12 highlights the Douglas Lake area. Old shorelines were
abandoned, new lands emerged, and new shorelines were cut as water levels fell.
The Riggsville Island spit that Krist and Schaetzl (2001) described is evident in
the north-central portion of the figure. Main, Ardtrea, and Upper Orillia
shorelines tend to be closely spaced, which suggests Upper Orillia waters were

the last to erode many shorelines in this area.

 

Figure 6.12: Areas in the Douglas Lake area that were predicted to be above
glacial Lake Algonquin water levels. This extent of this figure corresponds with
the extent of Figure 3.13. The image in this dissertation is presented in color.

272

The terrain near Charlevoix, Michigan, (Figure 6.13) is complex and
relatively difficult to interpret. Recall, Little Traverse Bay served as an outlet for
glacial Lake Chicago as water passed into the Indian River Lowlands and
drained into the Huron basin (Hansel et al., 1985). Leverett and Taylor (1915:426)
speculated glacial Lake Algonquin ”probably” extended up these valleys and left
”distinct shorelines around Pine Lake” (now called Lake Charlevoix) that ”mark
the highest Algonquin beach and some lower members of the upper group.”
These results support Leverett and Taylor’s claim, for Main, Ardtrea, and Upper
Group shorelines are very closely spaced in this area, particularly on the south
side of Little Traverse Bay, and their waters did extend into these valleys. As
glacial Lake Algonquin water planes tend toward convergence in this region,
long-term water level distributions begin to overlap each other more and more
(see Chapter 2, this volume, regarding long-term variability in lake levels). Few
areas appear to have emerged during the Upper Orillia phase; rather, it seems
that uplands in this region were last eroded by Upper Orillia waves (Larsen,
1987). Thus, evidence of the older and higher shorelines was likely destroyed by
wave action at the perirneters of later and lower lake planes. These
characteristics are generally consistent with a transgressive lake sequence. Large
areas appear to have emerged, however, as water level fell from the Upper
Orillia level to the Lower Orillia level. Water either withdrew from these valleys

and embayments, or left inland lakes behind.

273

8 Kilometers

5 Miles

 

Figure 6.13: Areas near Charlevoix that were predicted to be above glacial Lake
Algonquin water levels. This extent of this figure corresponds with the extent of
Figure 3.16. The image in this dissertation is presented in color.

The area south of Alpena, Michigan (Figure 6.20) provided similar
difficulties. Recall, Leverett and Taylor (1915) expressed great difficulty
attempting to identify distinctive water planes along the flat and sandy terrain
west of Alpena. Accordingly, glacial Lake Algonquin shorelines appear to
separate over vast distances across the sand plain despite close proximities
among elevations. The Main and all Upper Group shorelines are compactly

spaced and situated, however, at the base of a tall bluff south of Alpena.

274

0

Lake
. Huron

Thunder
Bay

 

Figure 6.14: Areas south of Alpena, Michigan, predicted to be above glacial Lake
Algonquin water levels. This extent of this figure corresponds with the extent of
Figure 3.20. The image in this dissertation is presented in color.

Leverett and Taylor (1915) described a ”lake cliff and upper ridge” that crosses
the Au Sable River ”4 miles west of Oscoda" (p.420). The Main, Ardtrea, and
Upper Orillia water planes were predicted to have elevations within 3 meters of
each other near Oscoda, Michigan (Figure 6.15); the Ardtrea and Upper Orillia
were predicted to intersect at 196.3 m. The upland area above the Main water
plane is the lower delta Burgis (1977) described that formed at the former mouth

of the Au Sable River in glacial Lake Algonquin waters.

275

 

 

Figure 6.15: Areas near Oscoda, Michigan, predicted to be above glacial Lake
Algonquin water levels. This extent of this figure corresponds with the extent of
Figure 3.22. The apparent line west of Oscoda marks the southern limit of the
study area. The image in this dissertation is presented in color.

Maps like those shown above can also be used to find areas that might
contain glacial Lake Algonquin features that have been overlooked. A good
example is a site in northwestern Kalkaska County, Michigan, where the Rapid
River exits the Inner Port Huron moraine (Figure 6.16). Interpretation of
topographic maps suggests a large outwash fan and / or delta formed at the
mouth of an outwash channel. Figure 6.16 shows a sequence of intersections
between the Main and Upper Group water planes and the contemporary ground
surface. From these results, it is reasonable to hypothesize that the morphology

of this feature might have been last shaped by glacial Lake Algonquin.

276

 

Figure 6.16. The Rapid River outwash fan/ delta during the: a) Main; b) Ardtrea;
c) Upper Orillia; and d) Lower Orillia phases. Pictured is a portion of the USGS
1:24,000 Torch River 7.5 Minute Series Quadrangle, but rescaled to 1:63,500 for
display. Darkened areas are predicted to have been under water at with 90%
confidence. The image in this dissertation is presented in color.

277

 

 

 

 

 

 

 

Figure 6.17. Pullup Lake and the surrounding area during the: a) Main; b)
Ardtrea; c) Upper Orillia; and (1) Lower Orillia phases. Pictured is a composite of
the USGS 1:24,000 Gilchrist and Roberts Corner 7.5 Minute Series Quadrangles,
but rescaled to 1:63,500 for display. Darkened areas are predicted to have been
under water at the 90% confidence level. This image is presented in color.

278

Other areas simply remain difficult to interpret. For example, the Main
and each of the Upper Group water planes apparently intersect the land surface
at or near Pullup Lake (see Figure 6.17), which straddles the Mackinac and Luce
County line and is situated at the northwest extent of available data. The land
surface exhibits gentle relief and no conspicuous shoreline feature, and water
plane elevations have been predicted with no better than + / - 3 m of precision (at
the 90% confidence level), so much of the area has fallen within overlapping
bands of uncertainty. One possible sequence of events, which is shown in Figure
6.17, suggests Pullup Lake was left stranded from glacial Lake Algonquin
sometime between the Ardtrea and Upper Orillia phases. This sequence is but
speculation because so much uncertainty about shoreline locations persists in
this area. Additional field work is required and, perhaps, an examination of lake
sediments might reveal information about the true locations and timing of these

events.

Summary

In this Chapter I presented maps of .four glacial Lake Algonquin lake
phases. These maps do not present deterministic answers to the question: where
are relict shorelines located? Instead, they summarize a range of possible results
and show areas where ancient shorelines probably occurred. Accordingly, I
needed to abandon the usual methods for representing shorelines and develop a

new and stochastic representation: bands of varying widths over which ancient

279

shorelines probably occurred. I refer to these bands as bands of uncertainty. The
width of a band of uncertainty is sensitive to two factors: uncertainty about the
vertical difference between the ground surface and a water plane; and slope
gradient. Uncertainty about the vertical difference between ground surface and
water plane elevations is driven by uncertainty about error in the DEM.

Narrow shoreline bands are associated with steep slopes, which retained
lake waters, and consistent classification results. Wide bands are associated with
gradual slopes and inconsistent classification results. I also mapped
uncertainties associated with the water plane models that support landscape
reconstructions. In short, I added a layer of ’fog’ to indicate where uncertainty
about the predicted water plane elevation exceeded certain thresholds.

Maps like those shown in Figures 6.9 to 6.15 can be created when a
particular confidence level is selected. For these figures, I selected and mapped
all areas that were predicted by my spatial model to be above water 90 times out
of 100 runs. Resultant ”shorelines” between above water and not above water areas
are then to be interpreted, not as the ”water’s edge” (Komar, 1998: 47), but as the
break between areas that were above water 90 percent of the time and areas that
were not above water 90 percent of the time. This probabilistic method is a new
way of looking at shorelines.

These results demonstrate the value of assessing spatial data quality,
modeling error propagation, and working with uncertainty in work that uses a

geographic information system (GIS) because it is the uncertainties, not the

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shorelines, that prompt new lines of inquiry. For example, the map of Upper
Orillia shorelines indicates the Upper Orillia water plane passes close to the
contemporary surface of Walloon Lake. I can tell the two are close because
uncertainty about error in the DEM has upset the classification process in this
region. Yet, had I used a simpler deterministic model, instead of the
cumbersome one I described in Chapter 5, it would have compared the
elevations along these two surfaces and rendered only one decision: yes, the
surface of Walloon Lake sits above the Upper Orillia water plane; or no, it does
not. But the datasets I employed are not perfect, complete, or precise, and my
spatial model can deal with that. In the end it is the uncertainty in my results
that prompts new line of inquiry: Was Walloon Lake really connected to glacial
Lake Algonquin during the Upper Orillia phase and stranded thereafter? If so,
does Walloon Lake contain organic materials suitable for radiocarbon dating? If
so, would the radiocarbon date help refine the Lake Algonquin chronology?
Had Walloon Lake not been mapped as a band of uncertainty, it would not have
drawn my attention and I would not have asked these questions.

Aerts et al., claim it is important to understand uncertainty when spatial
data and spatial models are used in decision-making processes ”where variation
in results may have profound implications” (Aerts et al., 2003: 251), particularly
decisions that influence human health and safety. Obviously, the variation that
exists in these results does not have profound implications for the health and

safety of persons living on or near glacial Lake Algonquin shorelines. But the

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ideas and methods used in this research can be adapted in work that focuses on
contemporary shorelines, where coastal development, population growth, and

land use changes occur without regard to the dynamic nature of the coastal zone.

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CHAPTER 7: CONCLUSIONS

Introduction

Nearly all .forms of data, information, and knowledge are imperfect, so
work that relies of geographic information systems should deal with uncertainty.
The purpose of this research has been to demonstrate the value of assessing
spatial data quality, dealing with uncertainty about errors in input data, and
visualizing uncertainties propagated through work conducted in a GIS
environment. The additional work required to add uncertainty components to a
spatial model is worth any elegance the model might lose because, paradoxically,
knowledge gained about uncertainties that propagate into results can reveal
valuable insights into the problem under investigation.

The demonstration is accomplished via a thoroughly worked example. In
short, I carefully reconstructed four differentially upwarped water planes and
four landscapes with isostatic depressions that are associated with glacial Lake
Algonquin - a sequence of pro-glacial lakes and a long-standing physiographic
and geologic problem. I recognized and modeled uncertainty along the way. In
this final chapter I consider the successes and weakness of this demonstration by
re-evaluating the research objectives in terms of the work accomplished. I also

propose new lines of inquiry and offer some concluding remarks.

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Re-evaluation of research objectives

To find and survey relict shoreline features that best serve as indicators of former lake
levels; and to conflate new paleoshoreline data with data collected during previous
mapping campaign.

I started by inheriting the glacial Lake Algonquin dataset that Schaetzl et
al. (2002) had assembled for northern Michigan. I retained most of their data
points for further analysis (126 of 146); the balance is stored in a supplemental
database. I expanded the study area to include relict shoreline features situated
in nearby Ontario and others in Michigan’s Upper and Lower Peninsulas; I
collected 69 new data points there. Elevation values I obtained at sites in the
Munuscong Islands region, near Douglas Lake, and near the Au Sable River
compliment the elevation values reported previously by Schaetzl et al. (2002) - so
it seems our efforts identified the same features and obtained similar elevation
values from them. I conflated data collected previously by Cowan (1985: 10
bluffs at Sault Ste. Marie) and Karrow (1987: 19 bluffs at St. Joseph Island) with
my own. The new elements of the glacial Lake Algonquin dataset fill large data
gaps (Cowan, 1985) and furnish new points of support for the restoration of
glacial Lake Algonquin water planes (Taylor, 1895). Individually, each sample
marks a point along a former shoreline. In aggregate, they outline several

distinct water planes within the region of interest: Main (57), Ardtrea (41), Upper

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Orillia (33), Lower Orillia (16), Wyebridge (12), Penetang (13), Cedar Point (17),
Payette (7), Sheguiandah (3), Korah (1) and others (43).

I relied on the Global Positioning System (GPS) to make measurements of
paleoshoreline positions. The GPS is being integrated with other forms of
technology (e.g., cell-phones, digital cameras, etc.) and used to support location-
based services (e.g., recreation, navigation, inventory tracking, etc). Popular
conceptions of the GPS, however, include false notions about how consistently it
can measure positions with a high degree of accuracy. The accuracy assessment
of GPS-derived position data in this work has shown that, yes, the GPS can be
used to achieve sub-meter measurement accuracy, but careful planning and
execution, and tedious data processing are required to minimize errors. GPS-
based position measurements are subject to several error processes that change
with location and time.

The features I surveyed at Cockburn Island are particularly important
features because they add much needed support near the northern rims of glacial
Lake Algonquin water planes. They also provide clues about the deglaciation
history of the area. We know that the Superior Lobe of the Laurentide ice sheet
retreated northeastwardly after reaching a maximum extent that covered the
northern portion of Michigan’s Lower Peninsula (Karrow, 1987 ; Blewett, 1995;
Larson and Schaetzl, 2001). Lakes in the Michigan and Huron basins were joined
when retreating ice uncovered the Indian River lowlands and, slightly later, the

Straits of Mackinac, which Larsen places at approximately 11,200 yr BP (after

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Hansel et al., 1985). Water levels in glacial Lake Chicago (Michigan basin)
dropped to the glacial Lake Algonquin level (Huron basin) upon joining (Hansel
et al., 1985), which left the outlet at Chicago abandoned (Hansel et al., 1985;
Larson and Schaetzl, 2001) and directed outflow to the Fenelon Falls outlets near
Kirkfield, Ontario (Finamore, 1985). Thus began the Main phase of glacial Lake
Algonquin. The presence of Main phase shorelines on Cockburn Island suggests
that the ice sheet retreated through Cockburn Island sometime during the early
portion of this lake phase; early enough to allow bluff cutting and shoreline
development processes to occur. Karrow (1987) concluded that St. Joseph Island
was deglaciated ”about11,000 yr BP or shortly thereafter” (p119). Cockburn
Island is situated along the same apparent isobase that runs through St. Joseph
Island (Figure 3.8), so both islands were likely deglaciated at approximately the
same time. Therefore, locations between the Straits of Mackinac and the
Cockburn Island-St Joseph Island region must have been deglaciated within,
roughly, a 200-year period. Main phase and lower shorelines on Cockburn Island
tell us that Cockburn Island was deglaciated before the outlets at North Bay,
Ontario, because lower lake phases are associated with falling water levels
brought about by deglaciation of the outlets at North Bay (Kaszycki, 1985;
Karrow, 1987). Karrow et al. (1975) reported radiocarbon dates that indicate
glacial Lake Algonquin, from the Main phase to the lowest, existed between
11,200 yr BP and 10,400 yr BP. Relict shoreline features at Cockburn Island are

important features because they help to locate the ice sheet margin, albeit

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roughly, as well as the northern extent Main Lake Algonquin within the context
of this short time frame.

Karrow (1987) and Larsen (1987) have noted the long-standing
controversy regarding whether certain water planes in the glacial Lake
Algonquin sequence are parallel, thus implicating changes in outlets were
responsible for changes in water levels, or whether they converge toward a
single outlet, which would implicate isostatic rebound as the sole cause of
shoreline deformation and change. This study has found evidence of
convergence between the Main and Ardtrea water planes, which agrees with the
earlier findings of Deane (1950) and Schaetzl et al. (2002). Proceeding
southwardly: Main and Ardtrea bluffs at Cockburn Island are vertically
separated by approximately 8 m (280 and 272 m, respectively); in the Munuscong
Islands region they are separated by ~7 m (265 and 258 m, respectively); on
Mackinac Island they are separated by ~6 m (242 and 236 m, respectively); and,
in the Douglas Lake area, they are separated by ~4 m (225 and 221 m,
respectively). Moreover, the Main and Ardtrea shorelines are difficult to
differentiate at locations south of Little Traverse Bay (Lake Michigan) and
Thunder Bay (Lake Huron) because they either occur within 3 m of each other or
they were reworked or destroyed by younger and lower lake phases.
Convergence between the Main and Ardtrea water planes suggests differential
uplift relative to the Fenelon Falls outlet was the cause of deformation and tilt

during the Main and Ardtrea phases.

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Areas north of Traverse City and south of Alpena are where the Main and
Ardtrea water planes tend toward convergence. In Ontario, Karrow reported the
Main Lake Algonquin shoreline between Kincardine and Port Elgin, along the
eastern shore of Lake Huron, ”has been entirely removed by later shore erosion
by lower water levels after the Main Algonquin level” (Karrow, 1987: 161). I
believe the same kind of bluff removal processes that occurred between
Kincardine and Port Elgin, Ontario, also occurred north of Traverse City and
south of Alpena, Michigan. Consequently, I also believe it makes good sense to
attribute observable shorelines in these areas to the last phase to act upon them;
not the first or the highest. Therefore, I can agree with Larsen's claims that Main
and Ardtrea shorelines of eastern Lake Huron predate the highest stranded
shorelines in northern Lake Michigan, and the apparent ”Main” shoreline of
Lake Michigan ”may correlate with the Orillia shoreline of Ontario” (Larsen,
1987 : 21). This does not mean that the Main or Ardtrea water planes did not
extend into the Michigan basin, for evidence at Beaver Island suggests they did;
it means only that many of the highest remaining glacial Lake Algonquin
shorelines in the Michigan basin correlate best with younger lake phases.

Upper Orillia shorelines occur consistently below Ardtrea shorelines at
Cockburn Island, the Munuscong Islands, Mackinac Island, and in the Douglas
Lake area, but a review of elevation differences between them provides
conflicting evidence regarding convergence. Thus, it was somewhat surprising

to find that the reconstructed Ardtrea and Upper Orillia water planes intersect

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near the mouth of the Au Sable River; the two models converge there at 196.3 m.
This finding should be treated as provisional, however, because the Upper
Orillia water plane model was supported by fewer data than was the Ardtrea
water plane model. Of the two, the Upper Orillia model was noisier, less precise,
and subject to the greatest uncertainties. I must also recognize that, after
working with these data, there might be some classification errors between the
closely-spaced Upper Orillia and Lower Orillia features in Michigan’s Lower
Peninsula, which would pull the reconstructed Upper Orillia water plane to
lower elevations. These features should be revisited.

The embayment that holds contemporary Walloon Lake (Lower Peninsula
near Charlevoix) was likely last connected to glacial Lake Algonquin during the
Upper Orillia phase. Perhaps future study of the oxygen isotOpe and pollen
records stored in sediments at the bottom of Walloon Lake might reveal
information about when the embayment separated from the lake, which could
then be used to bracket the time it took glacial Lake Algonquin to transition from
the Main to the Upper Orillia phase of its existence at that location.

Few sites contain multiple instances of later and lower water planes.
Cockburn Island and the Munuscong Islands region, for example, hold instances
of both the Upper Orillia and Penetang shorelines. The vertical difference
between these shorelines at Cockburn Island is 36 m, whereas the difference in
the Munuscong Islands region is only 30m. A decreasing separating distance

with decreasing latitude suggests convergence again, hence the influence of

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differential rebound. The difference between two points, however, is not
sufficient for characterizing the spatial pattern of difference between two water
planes, so no valid conclusion can yet be drawn about the relationship between
the Upper Orillia and Penetang water planes.

Evidence of convergence between particular water planes in northern
parts of the Huron basin notwithstanding, neither this research or the glacial
Lake Algonquin dataset can be used to resolve the question of where glacial Lake
Algonquin stood in the southern parts of the Huron and Michigan basins. No

data were collected there.

To reconstruct water planes associated with glacial Lake Algonquin lake phases.

This is the first work that has ever attempted to map the entire sequence
of ”Upper Group” (Deane, 1950) shorelines in this region. I have shown that
long-term variation in glacial Lake Algonquin water plane elevations can be
expressed as the sum of three components: a spatial trend that represents
isostatic recovery across the region; a random and spatially structured
component that captures localized effects (e. g., differential subsidence,
differential erosion, etc); and a random but spatially unstructured component
that captures chaotic variation. From these components, I built geostatistical
models to reconstruct four phases of glacial Lake Algonquin. Model parameters
quantify the rates at which water plane elevations increase with decreasing

distance toward the former center of ice loading. Parameter values decrease over

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time and indicate that younger water planes are warped less than older ones.
Water planes were reconstructed via universal kriging, which produced surfaces
of predicted water plane elevations that passed through supporting data, and
estimates of prediction uncertainty at every location. Locations where prediction
uncertainty exceeds three meters should be flagged for additional investigation.
The Main, Ardtrea, Upper Orillia, and Lower Orillia water plane surfaces
generated during this work (Figures 5.6a, 5.8a, 5.10a, and 5.12a) look similar to
the water plane surfaces derived from paleoshoreline data by Schaetzl et al.
(2002). The water plane models reported in this work, however, are superior to
the water plane models presented by Schaetzl et al. (2002) in five important
ways. First, each of my models is supported by more paleoshoreline data that
cover larger geographic extents. Recall, the geographic distribution of the
original glacial Lake Algonquin dataset was oriented roughly along the expected
trend and not normal to it. New paleoshoreline data were collected along an axis
normal to expected uplift trends to better capture these trends. Second, each of
my models incorporates data taken from Ontario, where Lake Algonquin
shorelines have long been recognized. Accordingly, bluff sites that were
rnisclassified by Schaetzl et al. (2002) and Farrand and Drexler (1985) were
reclassified (Chapter 3) and have been integrated into the findings reported by
Sly and Lewis (1969), Cowan (1985), and Karrow (1987). Third, I used a reduced
second-order trend model to capture the uplift trend; all model parameters were

found to be statistically significant. Schaetzl et al. (2002) used a full second-order

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model that retained a statistically insignificant term, which renders their model
as less meaningful. Fourth, my geostatistical rebound models take into account
both the broad regional uplift trend and localized deviations from that trend that
likely result from differences among site conditions; Schaetzl et al. (2002) focused
on the trend only. And fifth, before geostatistical analysis, I rescaled all location
coordinate values from the meter to the kilometer unit of measure, and
translated the planar coordinate system origin from a location outside the State
of Michigan to Traverse City, Michigan to reduce coordinate magnitudes. This
coordinate transformation mitigated rounding errors created during trend
surface analysis and by computer word overflows (Burrough and McDonnell,
1998) - especially when coordinate values were raised to powers greater than
one for use in second- or higher-order trend models. The full second-order trend
surface models reported by Schaetzl et al. (2002) were surely influenced by such
rounding errors and, therefore, the parameter coefficients obtained from them
cannot be considered accurate. Also, my trend model coefficients express rates
of uplift in m/ km, which is more user-friendly than the rates they reported in
m / m. In these five ways, the water plane models reported in this work are
superior to the water plane models presented by Schaetzl et al. (2002).

Glacial Lake Algonquin water planes are continuous, smooth, and show a
general pattern of uplift that tends to increase in Michigan from the southwest to
the northeast and towards the former centers of ice loading. The Lake

Algonquin water plane surfaces generated during this work (Figures 5.6a, 5.8a,

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5.10a, and 5.12a) also look similar to postglacial rebound surfaces derived by
others from lake gauge data (e.g., Coordinating Committee, 1977, 2001;
Tushingham, 1992; Mainville and Craymer, 2005), and from a geophysical model
(e.g., Tushingham and Peltier, 1991). The apparent similarities between mapped
contours that represent elevations along each glacial Lake Algonquin water
planes and Mainville and Craymer’s (2005) mapped isobases that show
contemporary rates of postglacial uplift suggest that my water plane models are
reasonable and, importantly, that the pattern of isostatic recovery has not
changed much during that last 11,000 years.

It has been customary in past and related research to construct lake-level
curves or shoreline diagrams along a line of profile that extends from a
recognizable place and is oriented in the expected direction of greatest uplift
(e.g., Goldthwait, 1910; Leverett and Taylor, 1915; Stanley, 1936; Farrand and
Drexler, 1985; Finamore, 1985; Karrow, 1987; and Larsen, 1987). Although I
constructed them, I do not report lake-level curves in this work because I have
come to believe such diagrams are inadequate and inappropriate for describing
deformation over large areas; they cannot depict important and meaningful
trends in plan, and they imply the direction of greatest uplift remained constant
over time. In my opinion, use of shoreline diagrams should be limited to
relatively small areas; those that span roughly no more than one degree of

latitude or longitude.

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Each of the water plane models presented in this work is a statistical
model, with a predicted elevation and variance at each grid cell location.
Accordingly, the distribution of elevation values at any location and a statistical
difi‘erence of means test can be used to estimate the probability that a bluff
elevation, perhaps one surveyed at a future date, might belong to a modeled lake
phase. The test result can be used to reject or fail to reject the null hypothesis of
unequal means and, hence, suggest a proper classification for the newly sampled
site. Moreover, in the presence of sound physical evidence for a bluff to belong
to a particular lake phase, a test result that fails to reject the null hypothesis
might indicate the statistical model should be updated to include information
obtained from the newly surveyed feature.

And last, co-located elevations along any two statistical lake surfaces can
be compared using a spatial version of the two-sample difference of means test. For
example, an apparent difference between the mean Main and Ardtrea water
plane elevations at a given location can be assessed for statistical significance
given the respective kriging variance around each predicted mean. Locations
where water planes converge should have mean elevations that are not
statistically different. Locations where different means are not statistically

different should be flagged for additional investigation.

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To reconstruct the landscape associated with each lake phases and map the distribution of
glacial Lake Algonquin shorelines.

I reconstructed four landscapes within a GIS environment using
combinations of digital water plane models and an error-prone digital elevation
model. This research has demonstrated that an analysis of elevation errors can
reveal artifacts of different DEM production methods, which in turn can be used
to partition the dataset into meaningful subsets. Elevation data that covered
Ontario, for example, were delivered with scant metadata; hypsometric analysis
revealed oversampled elevations that match contours on topographic maps, and
undersampled elevations that occur between mapped contours - clues that
implicate specific sources materials and interpolation methods. Also, analysis of
elevation errors and elevation derivatives, like slope gradient and slope aspect,
can be used to identify horizontal shifts in coordinate data. The National
Elevation Dataset (Gesch et al., 2002) may be the best available elevation dataset
for this region, but this research has shown the meaning of ”best” varies with
location.

This research has also demonstrated that uncertainty about errors in a
DEM can be modeled, incorporated into spatial model design, and used to reveal
locations where ”the result” is vulnerable to uncertainty and is, therefore,
indeterminate. The DEM employed in this work contains 25,718,215 grid cells;
only 529 elevations were tested (0.002%) but nearly all contained some amount of

error. It is reasonable, rational, even responsible to recognize that most of the

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other 25,717,686 elevation values are subject to uncertainty about elevation error.
Fortunately, DEM error, like many terrain properties, tends to exhibit spatial
autocorrelation. Spatial autocorrelation among data can be exploited; kriging
methods can be used to make informed predictions about error at each location;
and simulation techniques can be used to generate alternate possible realizations
of DEM error surfaces, which in turn can be applied as corrections to the original
DEM. The purpose of adding all of this cumbersome complexity to what might
otherwise be an elegant spatial model is to determine how vulnerable a
particular result is given uncertainty about error in the underlying data.
Uncertainty is unavoidable and comes in many forms; its impacts need to be

recognized and assessed.

To express the degree of uncertainty with which each glacial Lake Algonquin shoreline
location has been mapped.

This research began with the recognition that a linear object is an
imprecise representation of a shoreline because linear objects do not represent
the volumes of spaces in which natural variability in lake levels and associated
shoreline movements occur. Accordingly, this research has adopted a new form
of shoreline representation - a stochastic representation -- that embodies
uncertainty about shoreline location.

In recent work, MacEachren (2005) identified core challenges associated

with visualizing uncertainty in geospatial data; among them is ” the challenge of

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depicting multiple forms of uncertainty in the same display” (MacEachren, 2005:
156). This work has met that challenge. Glacial Lake Algonquin shoreline maps
depict one form of uncertainty that results from the interplay between beach
slope and uncertainty about error in the underlying DEM, and another form
associated with the spatial distribution of precision with which the underlying
water plane elevations had been predicted. Different visual cues express each
form of uncertainty and they work in conjunction with the results. Visual cues
allow the map reader to focus on the best parts of the map, identify locations on
the map where results are vulnerable to uncertainty, and to understand the
reasons for why a result at one location might be more or less reliable than at

another.

Future research

This research is intrinsically geographic because it synthesizes concepts,
knowledge, and tools from multiple disciplines to study a portion of the Earth. It
employs methods developed in the field of Geographic Information Science to
tackle a long-standing physiographic and geologic problem. Yet, because I was
trying to build a bridge between these specialties, I faced the constant challenge
of striking the right balance, or maybe the right juxtaposition, between efforts to
understand how uncertainty should be incorporated into a GIS environment and
efforts to understand a sequence of pro-glacial lakes. A strength of this work is

that each field provided a context for reflecting upon the other. A weakness is

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that opportunities to follow paths into one field were sometimes abandoned to
follow paths into the other. Consequently, I can think of many lines of inquiry

worth pursuing in the future.

Glacial Lake Algonquin

Although new data have been collected, relict features in Michigan’s
Upper Peninsula remain under-represented. More data should be collected to
resolve some of the uncertainty that persists regarding relict shorelines in that
area. The swampy nature of the terrain, private property, and a sparse road
network serve as effective barriers to exploration and data collection, but the
maps built during this research can be used to focus future exploration and data
collection activities. Data collected in the Upper Peninsula will furnish new and
valuable support to water plane reconstructions and can provide better ground
control for future DEM simulations.

This research has demonstrated again that a wave-cut bluff is an effective
indicator of a former water plane position. Yet, a weakness associated with
using bluffs as indictors is that they seldom occur in close proximity to each
other wherever water planes converge. The landscapes situated between
Petoskey and Traverse City, and between Alpena and the Au Sable River, remain
difficult to study because water planes trend toward convergence (the Ardtrea
and the Upper Orillia do converge) and each relatively old bluff record has likely

been reworked or destroyed by younger lake phases. New and better indicators

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are needed to mark glacial Lake Algonquin water planes in these troublesome
areas.

Maps of the ancient landscapes reveal several changes that merit study
beyond the scope of research presented here. For example, the apparent
outwash fan/ delta complex at the former mouth of the Rapid River (Kalkaska
County, MI) might have a sediment structure that can provide clues about past
lake events. The sediment and pollen records at the bottom of Walloon Lake
(Charlevoix County), an embayment that separated from glacial Lake Algonquin
after the Upper Orillia phase, might hold clues about the timing of that
separation and, hence, the timing of the Upper and Lower Orillia phases. And,
the cedar swamps that bracket the Penetang and Cedar Point shorelines at
Cockburn Island (Ontario) might hold organic materials suitable for radiocarbon
dating of those phases.

Like newly sampled bluffs, the elevations of small inland lake surfaces
and bottoms can be compared statistically to co-located elevations along the
glacial Lake Algonquin water planes. Difference of means tests can be used to
assess whether an inland lake is higher (older), lower (younger) or coincident (in
both space and time) with a given lake phase. Of course, statistical test results
are subject to their own forms of uncertainties, but they provide some grist for

rational decision making.

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Topographic map analysis

Topographic maps are commonly used to support geographic and
geologic explorations. Mapped contours are used to identify landforms and
landform assemblages, as they were during the initial stages of this work. The
differentially-upwarped water plane models reported in Chapter 5 can be
mathematically inverted and used to differentially-depress a DEM. New contour
lines can be constructed from the adjusted DEM, which might reveal landform
characteristics that are not depicted in the contemporary representation, or slope
gradients that suggest, for example, the overland flow of water moved

differently than it would today.

Visualizing uncertainty

I invested much effort into understanding, modeling, and depicting
uncertainty in my data, models, and results; doing so surely kept me close to the
data and prevented me from trusting software. Yet, I do not know whether or
not my depictions will actually aide others who are interested in this line of work
(another form of uncertainty!) Will the indicators of uncertainty be ignored? Or,
will any tinge of uncertainty prompt the reader to reject all results out of hand?
The GIScience literature provides little guidance about which depictions of
uncertainty are best, or how map readers respond to mapped uncertainties.
More cartographic research is needed at the cognitive level to find answers to

these questions and provide guidance.

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Global climate change and sea-level rise

This research focused on an analysis of ancient shorelines in the upper
Great Lakes basin. Yet clearly, the ideas and methods it employs can also be
applied in other work that uses GIS to model paleolake sequences (e. g., Lake
Agassiz , Lake Barlow-Ojibway, etc), or to study contemporary issues regarding
coastal environments.

A major threat of global climate change is the expected rise in global sea-
level. Many human populations and economic infrastructures are situated in
low-lying coastal environments and vulnerable to flood and inundation. Much
work is already underway to identify flood-prone areas and to prioritize them
according to the degree of perceived risk; many are using a GIS and digital
elevation models to find locations under elevated water planes (e. g., Titus and
Richman, 2001; Simas et al., 2001; Cowell and Zeng, 2003; and Hennecke et al.,
2004), but only a few are integrating data quality assessments, uncertainty, or
simulation into the work (e. g., Cowell and Zeng, 2003; and Hennecke et al.,
2004). The concepts of vulnerability and risk embody the very idea of
uncertainty, and so too should related work with spatial data and GIS. Failure to
recognize uncertainty in the concepts, data, and models that support analysis of

global sea-level rise will surely fail to identify all areas that are at risk.

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Final thoughts

At the very beginning of this research I knew that data errors,
inaccuracies, or imprecision are customarily absorbed into many analyses. The
logic is usually something like -- it is impossible, impractical, or too costly to find
and correct every little error in a dataset, so, do your best to recognize pitfalls,
but move forward. Yet, of the many lessons I learned during my doctoral
research, the one that has made the biggest impression is learning just how
sensitive results can be to the slightest error - either in input data or
assumptions. For example, in terms of a given glacial Lake Algonquin water
plane, a meter of uncertainty in predicted water surface elevation and a co-
located meter of uncertainty in ground surface elevation, when combined, might
produce a kilometer of uncertainty regarding the location of the former land and
water interface. For another, in terms of a SOD-kilometer line segment extending
S72°E from Mackinac Island (the terminus of which would land on Ontario’s
Bruce Peninsula), a single degree of uncertainty in the generally accepted
direction of maximum isostatic uplift at Mackinac Island would (assuming a
linear uplift trend) subtend a 10.47 km (6.5 mi) arc of uncertainty in the terminus
location. In both examples, larger uncertainties in the inputs would result in
larger uncertainties in the outputs. Of course, uncertainties compound in such
ways in part because of the relatively large area covered by glacial Lake
Algonquin, but this work is hardly unique in its scale of analysis. Many such

uncertainties likely remain unexamined in other work.

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In addition to recognizing uncertainty, this research has allowed me to
learn methods for dealing with uncertainty. Monte Carlo simulation techniques
can be used very effectively to reveal ranges of possible outcomes and I find I
employ them more and more frequently, particularly when I undertake any
analysis that requires use of a DEM.

This research has provided me with invaluable opportunities to explore
landscapes once foreign to me; ancient and contemporary. I found great
satisfaction in exploring the Upper Great Lakes, particularly when I entered field
sites first described by James Goldthwait, Frank Leverett, or Frank Taylor, and I
was still able to see what they observed 100 years ago. I developed a deep
respect and appreciation for the detailed work they accomplished at the turn of
the twentieth century (although, after reading Lawson’s (1898) report, I think the
cleared landscapes of the timber-boom era offered them a few vantage points
that no longer exist today). Until recently, I did not appreciate the glacial history
of my hometown, North Tonawanda, New York. For example, I had always
thought a road near my house had been named, perhaps, by a comedic politician,
rather than for an actual beach ridge that formed along the shore of glacial Lake
Tonawanda, which I have begun to study. As a kid I thought I knew the nearest
beach was a forty-minute drive away -- I never considered a lake had once
covered much of my hometown. I now explore Western New York with a brand

new set of eyes.

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APPENDICES

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APPENDIX A: THE GLACIAL LAKE ALGONQUIN DATASET

Table A.1: The glacial Lake Algonquin dataset.

SID Longitude

Latitude

H Phase

Surveyed by:

USGS Quadname

 

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

-85.63302366

-85.60231784

-85.56937309

-85.58865547

-85.62899645

-8566830344

-85.73049857

-85.09660453

-85.09372479

-8508827092

-8506883233

-8507880280

-85.10439545

-85.13856504

-85.18779164

-85.32408926

-8532237124

-85.32252291

4500334624

45.04332913

45.05697549

45.07031354

45.16615307

45.12257434

45.01907969

4535397611

45.35500076

45.35584481

4528293080

45.28504629

4528015334

45.36462996

4532784476

44.96835341

44.91577464

44.91739619

199.5 Upper Orillia
199.3 Upper Orillia
196.8 Lower Orillia
196.4 Lower Orillia
198.0 Lower Orillia
203.0 Supplemental
194.2 Supplemental
212.9 Ardtrea

213.3 Ardtrea
213.0 Ardtrea
206.4 Upper Orillia
208.4 Upper Orillia
186.3 Nipissing
211.6 Upper Orillia
207.8 Upper Orillia
192.2 Supplemental
193.7 Supplemental

193.5 Supplemental

305

Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)

Drzyzga (this work)

Gills Pier MI
Omena MI
Omena MI
Omena MI
Northport NW MI
Gills Pier MI
Gills Pier MI
Bay Shore MI
Bay Shore MI
Bay Shore MI
Bay Shore MI
Bay Shore MI
Bay Shore MI
Ironton MI
Ironton MI
Alden MI
Alden MI

Alden MI

SID
119

122

123

124

125

126

127

128

129

130

131

132

133

136

137

138

139

140

141

142

143

Logitude
-85.32154529

-83.45362909
-83.45106651
-83.43179963
-83.42798820
-83.35134954
~83.33455407
-83.33573016
-83.33781383
-83.34320991
-83.30577735
-83.29547761
-83.29397249
-83.34183811
-83.34188721
-83.33962682
-83.33416549
-83.33468861
-83.33508133
-83.33731193

—83.34322871

Latitude
44.91647656

44.40797866

44.40359657

44.44200397

44.45051694

4592652966

45.91880168

4591869340

4592006442

4592318112

4593664500

45.93210483

45.92815920

4591501164

4591466539

4591334400

4591442885

4591447228

4591237384

45.92213802

45.92317229

H Phase
185.5 N ipissing

196.5 Upper Orillia
193.4 Supplemental
196.3 Upper Orillia
196.8 Upper Orillia
257.1 Lower Orillia
270.6 Ardtrea
282.8 Main

287.6 Supplemental
289.4 Supplemental
225.4 Cedar Point
228.3 Penetang
223.9 Cedar Point
278.4 Main

272.9 Ardtrea

274.1 Supplemental
278.7 Main

284.0 Supplemental
281.4 Main

270.3 Ardtrea

291.0 Supplemental

306

Surveyed by:
Drzyzga (this work)

Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)

Drzyzga (this work)

USGS Quadname
Alden Ml

Foote Site Village
Foote Site Village
Foote Site Village
Foote Site Village
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W
Alpena-W

Alpena-W

 

SID Longitude Latitude H Phase Surveyed by: USGS Quadname
144 -83.34363020 45.92164571 281.5 Main Drzyzga (this work) Alpena-W

145 -83.34721044 4591774749 265.8 Upper Orillia Drzyzga (this work) Alpena-W

146 -83.31282193 4588670837 229.8 Penetang Drzyzga (this work) Alpena-W

147 -83.30608526 4589051522 2258 Cedar Point Drzyzga (this work) Alpena-W

148 -83.31027677 4588818884 225.8 Cedar Point Drzyzga (this work) Alpena-W

149 -83.31094088 4588840274 231.0 Penetang Drzyzga (this work) Alpena-W

150 -83.32045596 4588144630 229.6 Penetang Drzyzga (this work) Alpena-W

151 -83.32055222 4588096144 221.5 Cedar Point Drzyzga (this work) Alpena—W

152 -83.34188074 4591780072 280.4 Main Drzyzga (this work) Alpena-W

153 -83.34374321 4591787262 272.4 Ardtrea Drzyzga (this work) Alpena-W

154 -83.33678089 4592058486 280.0 Main Drzyzga (this work) Alpena-W

155 -83.33602752 4592064461 270.7 Ardtrea Drzyzga (this work) Alpena-W

156 -83.35121893 45.92486486 266.6 Upper Orillia Drzyzga (this work) Alpena-W

157 —83.35063026 4592946412 261.3 Lower Orillia Drzyzga (this work) Alpena-W

158 -83.35743306 4586297615 222.1 Cedar Point Drzyzga (this work) Alpena-W

159 —85.57144067 4565039861 223.2 Ardtrea Drzyzga (this work) Beaver Island North
160 -85.56099611 4564079801 225.1 Ardtrea Drzyzga (this work) Beaver Island North
161 -85.60102805 4558783750 212.5 Wyebridge Drzyzga (this work) Beaver Island South
162 -85.57687948 4565082847 229.3 Main Drzyzga (this work) Beaver Island North
163 -85.5506143O 4563533858 230.3 Main Drzyzga (this work) Beaver Island North
164 -8559166373 4559503977 211.4 Wyebridge Drzyzga (this work) Beaver Island South

307

 

SID Longitude Latitude H Phase Surveyed by: USGS Quadname
165 -8560005708 4558858628 214.0 Wyebridge Drzyzga (this work) Beaver Island South
166 -84.39957291 46.24582720 222.3 Cedar Point Drzyzga (this work) Pickford NW MI
167 -84.40278195 46.25272000 224.5 Cedar Point Drzyzga (this work) Dafter MI

168 -84.40771905 46.26127845 223.8 Cedar Point Drzyzga (this work) Dafter MI

169 -84.52817275 46.09691993 264.3 Main Drzyzga (this work) PontchartrainShores
170 -84.46171093 46.08546835 268.2 Main Drzyzga (this work) Hessel MI

171 —84.51391141 46.12579042 259.7 Ardtrea Drzyzga (this work) Rudyard MI

172 -84.51522788 46.12571287 266.9 Main Drzyzga (this work) Rudyard MI

174 -84.35074705 46.10030093 252.2 Upper Orillia Drzyzga (this work) Pickford Se MI
178 -84.67800346 4556689190 227.4 Main Drzyzga (this work) Indianville MI
180 -84.71894887 4556974785 222.2 Ardtrea Drzyzga (this work) Indianville MI
181 -84.73761887 4556823962 224.1 Ardtrea Drzyzga (this work) Indianville MI
182 -84.72269172 4552825547 223.8 Main Drzyzga (this work) Indianville MI
184 -84.69642609 4552827872 187.6 Nipissing Drzyzga (this work) Indianville MI
185 -84.62606253 4553077935 211.8 Wyebridge Drzyzga (this work) Indianville MI
186 -84.62612251 4552931520 198.8 Supplemental Drzyzga (this work) Indianville MI
201 —83.99226000 46.18304000 266.4 Upper Orillia Karrow (1987) Blind River—W
202 -83.99161000 46.18330000 272.2 Ardtrea Karrow (1987) Blind River-W
203 -83.98939000 46.18425000 279.6 Main Karrow (1987) Blind River-W
204 -83.96704000 46.17608000 279.4 Main Karrow (1987) Blind River-W
205 ~83.94314000 46.14960000 229.4 Cedar Point Karrow (1987) Blind River-W

308

 

SID Longitude Latitude H Phase Surveyed by: USGS Quadname
206 -83.99543000 46.20719000 231.8 Penetang Karrow (1987) Blind River-W

207 -83.97798000 46.22210000 277.4 Ardtrea Karrow (1987) Blind River-W

210 -83.99223000 46.21496000 259.2 Lower Orillia Karrow (1987) Blind River-W

211 -83.98233000 46.21939000 266.0 Upper Orillia Karrow (1987) Blind River-W

212 —84.04024000 46.18748000 282.9 Main Karrow (1987) Sault Sainte Marie-E
214 -84.04283000 46.19030000 211.6 Payette Karrow (1987) Sault Sainte Marie-E
216 —84.01131000 46.19021000 235.4 Penetang Karrow (1987) Sault Sainte Marie-E
217 -84.01152000 46.19052000 231.0 Penetang Karrow (1987) Sault Sainte Marie-E
220 -84.00889000 46.19139000 233.2 Penetang Karrow (1987) Sault Sainte Marie-E
221 -84.00843000 46.19105000 236.9 Penetang Karrow (1987) Sault Sainte Marie-E
223 -83.88658000 46.25011000 229.2 Supplemental Karrow (1987) Blind River-W

225 «8388925000 46.25373000 205.3 Sheguiandah Karrow (1987) Blind River—W

226 -83.42700000 46.27742000 257.0 Cedar Point Karrow (1987) Blind River-W

229 -83.42293000 46.27994000 242.3 Payette Karrow (1987) Blind River-W

230 -83.41440000 46.28120000 216.1 Korah Karrow (1987) Blind River-W

301 -84.61732000 4585397000 226.4 Supplemental Schaetzl et al. (2002) Round Island MI
302 -84.61689000 4585634000 236.3 Ardtrea Schaetzl et al. (2002) Round Island MI
304 -84.42874000 46.04946000 244.2 Upper Orillia Schaetzl et al. (2002) Hessel MI

305 -84.61326000 4586035000 227.4 Upper Orillia Schaetzl et al. (2002) Round Island MI
306 -84.6143000O 4586105000 229.2 Upper Orillia Schaetzl et al. (2002) Round Island MI
307 -84.61673000 4585712000 242.0 Main Schaetzl et al. (2002) Round Island MI

309

 

SID Longitude Latitude l-I Phase Surveyed by: USGS Quadname
308 -84.88870000 4569295000 233.9 Main Schaetzl et al. (2002) Bliss MI

309 -84.88881000 45.69346000 221.2 Upper Orillia Schaetzl et al. (2002) Bliss MI

310 -84.91972000 4570072000 232.7 Main Schaetzl et al. (2002) Bliss MI

311 -84.93121000 4567052000 231.9 Main Schaetzlet al. (2002) Bliss MI

312 -84.93156000 4566732000 230.2 Main Schaetzlet al. (2002) Bliss MI

313 -85.11090000 4556785000 224.4 Main Schaetzlet al. (2002) Good Hart MI
314 -85.11102000 45.56797000 221.8 Ardtrea Schaetzl et al. (2002) Good Hart MI
315 -85.03678000 4544465000 222.4 Main Schaetzl et al. (2002) Forest Beach MI
316 -84.93290000 4543185000 215.9 Ardtrea Schaetzl et al. (2002) Harbor Springs MI
317 -84.42160000 46.05165000 256.2 Ardtrea Schaetzl et al. (2002) Hessel MI

319 -84.50916000 46.13939000 241.4 Lower Orillia Schaetzl et al. (2002) Rudyard MI
320 -84.50916000 46.14145000 236.9 Wyebridge Schaetzl et al. (2002) Rudyard MI
321 -84.50952000 46.14325000 219.5 Supplemental Schaetzl et al. (2002) Rudyard MI
322 8456758000 4560592000 224.6 Ardtrea Schaetzl et al. (2002) Mullett Lake MI
323 -84.58870000 4552021000 212.8 Wyebridge Schaetzl et al. (2002) Mullett Lake MI
324 -84.59014000 4550540000 231.2 Supplemental Schaetzl et al. (2002) Mullett Lake MI
325 -84.59833000 4551805000 225.1 Main Schaetzlet al. (2002) Mullett Lake MI
326 -84.65294000 4553869000 210.6 Wyebridge Schaetzl et al. (2002) Indianville MI
327 -84.67479000 4555726000 229.3 Main Schaetzl et a1. (2002) Indianville MI
328 -84.71226000 4552652000 221.6 Ardtrea Schaetzl et al. (2002) Indianville MI
329 -84.80139000 4557997000 225.0 Main Schaetzl et al. (2002) Pellston MI

310

 

 

SID Longitude Latitude H Phase Surveyed by: USGS Quadname
330 8484149000 4568009000 232.5 Main Schaetzl et al. (2002) Levering MI

333 -84.62920000 4566410000 226.1 Ardtrea Schaetzlet al. (2002) Freedom MI

334 -83.62305603 4532519387 210.4 Supplemental Schaetzlet al. (2002) Thompsons Harbor
335 —83.59894435 4525779824 219.6 Ardtrea Schaetzl et al. (2002) Thompsons Harbor
341 -84.45442644 4547459575 225.9 Main Schaetzl et al. (2002) Legrand MI

342 -84.19049326 4540898973 225.5 Main Schaetzl et al. (2002) Black Lake Bluffs
343 -84.13565017 4542469734 228.0 Main Schaetzl et al. (2002) Black Lake Bluffs
344 -84.13851006 4542464758 219.0 Upper Orillia Schaetzl et al. (2002) Black Lake Bluffs
356 -84.20202880 4549575522 220.2 Upper Orillia Schaetzl et al. (2002) Black Lake Bluffs
357 -84.21784849 4552079069 227.3 Main Schaetzl et al. (2002) Grace MI

358 -84.22302439 4552256839 229.5 Main Schaetzl et al. (2002) Grace MI

359 -84.22880504 4543421460 209.5 Wyebridge Schaetzl et al. (2002) Black Lake Bluffs
360 -84.08819982 4540879539 222.7 Ardtrea Schaetzl et al. (2002) Ocqueoc MI

361 -84.08810804 4540886362 225.4 Main Schaetzl et al. (2002) Ocqueoc MI

362 -84.04832592 4546319257 218.5 Supplemental Schaetzl et al. (2002) Ocqueoc MI

363 -84.04778740 4546284301 227.5 Main Schaetzl et al. (2002) Ocqueoc MI

364 -84.04769782 4546213165 227.8 Main Schaetzlet al. (2002) Ocqueoc MI

367 —83.98904505 4545278767 229.4 Main Schaetzlet al. (2002) Moltke MI

368 -83.88414029 4539936502 222.9 Ardtrea Schaetzl et al. (2002) Moltke MI

369 -83.82380683 4538785866 225.7 Main Schaetzl et al. (2002) Rogers City MI
370 -83.69338766 4533825394 206.5 Supplemental Schaetzl et al. (2002) Posen MI

311

 

SID Longitude Latitude H Phase Surveyed by: USGS Quadname
371 -84.67629206 46.44486940 270.2 Upper Orillia Schaetzl et al. (2002) Dollar Settlement
372 -84.74021453 46.43716052 259.7 Lower Orillia Schaetzl et al. (2002) Dollar Settlement
374 -84.74495853 46.43867465 231.3 Cedar Point Schaetzl et al. (2002) Dollar Settlement
375 -84.64920303 4557800168 224.3 Ardtrea Schaetzl et al. (2002) Indianville MI

376 -84.74911461 4537772823 215.0 Ardtrea Schaetzl et al. (2002) Burt Lake MI

377 -84.63313100 4544144764 211.2 Supplemental Schaetzl et al. (2002) Burt Lake MI

378 -84.58903554 4542530622 207.4 Wyebridge Schaetzl et al. (2002) Indian River MI

379 -84.57091213 4542319758 218.2 Ardtrea Schaetzl et al. (2002) Indian River MI

381 -84.71036395 4537740598 214.4 Ardtrea Schaetzl et al. (2002) Burt Lake MI

382 —84.77874610 4538385287 223.0 Main Schaetzl et al. (2002) Alanson MI

383 -84.77755629 4538321676 217.8 Ardtrea Schaetzl et al. (2002) Alanson MI

385 —84.83107870 4543714322 225.3 Supplemental Schaetzl et al. (2002) Alanson MI

386 -84.80538259 4553183628 222.1 Ardtrea Schaetzl et al. (2002) Pellston MI

387 ~84.80544307 4553189694 223.4 Main Schaetzl et al. (2002) Pellston MI

388 -84.70242937 4561685275 229.7 Main Schaetzl et al. (2002) Indianville MI

389 -84.40614855 4625881886 221.2 Cedar Point Schaetzl et al. (2002) Dafter MI

390 -84.92605951 4555080838 223.6 Main Schaetzl et al. (2002) Larks Lake MI

391 -84.90655181 4644482623 234.5 Penetang Schaetzl et al. (2002) McNearney Lake MI
392 -84.90681053 4643164950 261.1 Lower Orillia Schaetzl et al. (2002) McNearney Lake MI
393 -84.90723553 4642600783 281.9 Main Schaetzl et al. (2002) McNearney Lake MI
395 -84.21857808 4648512906 240.2 Payette Schaetzl et al. (2002) Baie de Wasai MI

312

SID

Longitude

Latitude

H Phase

Surveyed by:

USGS Quadname

 

396

397

398

399

400

401

402

403

404

406

407

409

410

412

415

416

417

418

419

420

421

8421825660

8445054458

8445045627

8347505515

8347477603

8463595218

8352638080

84.82851886

84.83609532

84.74408419

8421838987

8332930199

8340495598

8342845631

8331709229

8330402450

8329081057

8347441160

8355748810

8355755667

8358602001

4645945842

4547556791

45.47174045

45.18305170

45.18315549

4643961387

44.96914845

4643381986

4642109801

4638566303

4648460739

44.78509654

4513449345

4444738975

4460621500

4474327233

4470767625

4523744780

4522256920

4522479077

45.21953387

228.8 Sheguiandah
217.2 Upper Orillia
221.8 Ardtrea
213.4 Upper Orillia
210.6 Wyebridge
240.4 Penetang
209.9 Ardtrea
230.2 Cedar Point
259.5 Lower Orillia
272.2 Ardtrea
241.2 Payette

197.7 Lower Orillia
214.2 Upper Orillia
196.0 Upper Orillia
199.2 Upper Orillia
195.6 Lower Orillia
194.0 Lower Orillia
157.1 Supplemental
217.7 Supplemental
201.6 Supplemental

221.6 Main

313

Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)

Schaetzl et al. (2002)

Baie de Wasai MI
Legrand MI
Legrand MI

Long Lake East MI
Long Lake East MI
Dollar Settlement
Big Ravine Creek
Pendills Lake MI
Pendills Lake MI
Dollar Settlement
Baie de Wasai MI
Black River MI
Long Lake East Ml
Foote Site Village
Greenbush MI
Harrisville MI
Harrisville MI
Long Lake East MI
Long Lake West MI
Long Lake West MI

Long Lake West MI

 

SID
422

426

430

431

432

435

436

440

441

442

443

445

446

447

448

449

450

451

452

453

454

Longitude
8348511400

8330301677
8342333174
8342505556
8345062220
8342503845
8330298278
8519560860
8515435504
8517520487
8497784297
8478927924
8484366807
8472485788
8436269308
8433750218
84.40501602
8444699546
8446699744
8421703213

8502418164

Latitude
4493197274

4464424244

4487308497

4487319590

44.90216957

4487325454

4464430982

4609898741

4610454764

46.06371179

4617370048

4611430390

4609717148

4611805526

4608904251

4610228830

4607400022

46.07161098

4605520906

4645848640

4633678241

H Phase
209.4 Ardtrea

189.5 Supplemental
209.0 Ardtrea

214.0 Main

211.9 Ardtrea

213.9 Main

190.2 Supplemental
249.2 Main

250.8 Main

214.6 Supplemental
259.1 Main

257.7 Main

239.1 Upper Orillia
245.4 Upper Orillia
249.5 Upper Orillia
227.0 Supplemental
258.4 Ardtrea
265.7 Main

241.4 Upper Orillia
228.2 Sheguiandah

276.8 Supplemental

314

Surveyed 13!:
Schaetzl et al. (2002)

Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)
Schaetzl et al. (2002)

Schaetzl et al. (2002)

USGS Quadname
Ossineke MI

Harrisville MI
Spruce MI
Spruce MI
Ossineke MI
Spruce MI
Harrisville MI
Epoufette MI
Epoufette MI
Epoufette MI
Ozark MI
Ozark SE MI
Ozark SE MI
Charles MI
Pickford SE MI
Pickford SE MI
Hessel MI
Hessel MI
Hessel MI

Baie de Wasai MI

Eckerman MI

 

SID Longitude Latitude H Phase Surveyed by: USGS Quadname
455 8503058381 4635106008 259.7 Upper Orillia Schaetzl et al. (2002) Eckerman MI

456 8506933171 4641646149 249.0 Wyebridge Schaetzl et al. (2002) Piatt Lake MI

457 8508359452 4642155634 258.0 Lower Orillia Schaetzl et al. (2002) Piatt Lake MI

458 8509491566 4649957572 233.6 Penetang Schaetzl et al. (2002) Piatt Lake MI

459 8511635073 4647715490 276.7 Supplemental Schaetzl et al. (2002) Piatt Lake MI

460 8522599496 4647753561 261.0 Lower Orillia Schaetzl et a1. (2002) Big Beaver Creek MI
461 8500674669 4638988785 255.7 Lower Orillia Schaetzl et al. (2002) Piatt Lake MI

463 8427014191 4555388648 229.7 Main Schaetzl et al. (2002) Manning MI

464 8420690114 4550243140 217.2 Supplemental Schaetzl et al. (2002) Grace MI

465 8421234800 4550911718 221.7 Upper Orillia Schaetzl et al. (2002) Grace MI

466 84.54980477 4557589774 225.6 Ardtrea Schaetzl et al. (2002) Mullett Lake MI
467 8455853828 4559495159 226.2 Ardtrea Schaetzl et al. (2002) Mullett Lake MI
468 8461109548 4564852333 231.2 Main Schaetzl et al. (2002) Point Nipigon MI
469 8461092475 4564875361 227.4 Ardtrea Schaetzl et al. (2002) Point Nipigon MI
470 8460114369 45.63751326 230.6 Main Schaetzl et al. (2002) Point Nipigon MI
471 8459611067 4563766964 233.4 Main Schaetzl et al. (2002) Point Nipigon MI
472 8445442526 4547459652 225.8 Main Schaetzl et al. (2002) Legrand MI

501 8435307774 4658282675 307.3 Main Cowan(1985) Sault Sainte Marie-E
507 8434384520 4656875261 247.7 Payette Cowan (1985) Sault Sainte Marie-E
508 8434392283 4656983441 254.4 Cedar Point Cowan (1985) Sault Sainte Marie-E
516 8438323813 4656642152 247.2 Payette Cowan (1985) Sault Sainte Marie-E

315

 

SID
517

522

523

524

525

526

991

992

993

994

995

996

997

998

Longitude
8438334252

8441477525
8441492481
84.41616848
8441719644
8441759403
8335040849
8335014286
8335018783
8335023280
8343138274
8343335401
8334475011
8337191795

8345614737

Latitude
4656696391

4656182938

46.56417276

4656546089

4656854412

4657116310

4592941133

4592930711

4592904659

4592878607

4447595453

4447579292

4595382812

4594480089

4440725030

H Phase
253.7 Cedar Point

243.8 Payette

253.5 Cedar Point
2645 Penetang
275.3 Wyebridge
290.9 Upper Orillia
261.4 Supplemental
265.6 Supplemental
267.0 Supplemental
268.4 Supplemental
204.3 Supplemental
211.4 Supplemental
222.0 Supplemental
241.9 Supplemental

203.0 Supplemental

316

Surveyed by:
Cowan (1985)

Cowan (1985)
Cowan (1985)
Cowan (1985)
Cowan (1985)
Cowan (1985)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)
Drzyzga (this work)

Drzyzga (this work)

USGS Quadname
Sault Sainte Marie-E

Sault Sainte Marie-E
Sault Sainte Marie-E
Sault Sainte Marie-E
Sault Sainte Marie-E
Sault Sainte Marie-E
Alpena-W
Alpena-W
Alpena-W
Alpena-W

Foote Site Village
Foote Site Village
Alpena-W
Alpena-W

Foote Site Village

 

APPENDIX B: SCRIPTS WRITTEN FOR USE WITH R

This appendix contains four scripts that were written for use in the R
environment for statistical computing. The first two (i.e., first.R and second.R,
supported exploratory data analysis and were used to build initial water plane
models via ordinary and generalized least squares, respectively. The third

(third.R) supported cross-validated assessment of the generalized model. And

 

the fourth script (i.e., predictWaterplane.R) makes the final predictions and
reconstructs the ancient water plane via universal kriging.

These scripts deal specifically with my efforts to model the Main phase of
Lake Algonquin. They were not written to be used once only; rather, they were
edited and tweaked dozens of times during the lengthy and iterative process of
building the final prediction model. Interactive exploratory and diagnostic
analyses were usually conducted before and after each run. The general
structure of each script was adapted for re-use during subsequent efforts to build

water plane models for lower and younger lake phases.

317

###########################################################
first.R

Scott A. Drzyzga
Summer 2006

Purpose: to model a differentially-uplifted water plane and estimate
parameters that describe rates of uplift. This script can be adapted
for use with other water plane data.

Dependencies (packages):
gstat, geoR, and sp.

Dependencies (objects):
main: a data.frame object that contains paleoshoreline position
data.
distance.R: an script that defines an R function to calculate an
interdistance matrix for a sample of points.

##########################################################

Specify the form of the ordinary least squares model.

####4t3t4t¢t4t#¢t#it4t¢t4t#4t4t#1t¢t¢t

main.formula <- z~x+I(x*y)+I(x"2)+I(y"2)

#

# Create and format main.xyz for simple and easy use.

#

main.xyz <- as.data.frame(cbind(main$SID, main$E, main$N, main$H))
colnames(main.xyz) <- cbind("SID","E","N","z")

#

# Scale and transform MIGEOREF coordinates (In) to a local coordinate
# system (local origin and km units of measure).

#

main.xyz$x <- (main.xyzSE - 532000) / 1000
main.xyzSy <- (main.xyszN - 468000) / 1000

#

# Calculate the inter-distance matrix

#

source("C:/ rdata/ phd/ waterplanes/ distance.R")
distmat <- calc.dist.mat(main.xyz$x, main.xyzSy)
#

318

Initial water plane model estimated via Ordinary Least Squares (OLS)
Plot residuals - stop to examine model fit, significance and check run
other diagnostics interactively.

##it-‘nltil:

main.ols <- lm(formula=main.formula, data=main.xyz)
main.xyz$olsr <- main.ols$residuals

qq.plot(main.xyz$olsr)

summary(main.ols$residuals)

#

# Perform variography of OLS residuals.

# Distance units are in km, elevation units are in meters.
# Explore, visualize, and assess interactively.

#

main.geo <- as.geodata(main.xyz, coords.col=5:6, data.col=7)
main.var <- variog(main.geo, option="bin", pairs.min=6, direction=110, ~
tolerance=45, unit.ang1e="degrees", max.dist=100, breaks=seq(from=0, to=60, ~

by=range))
#

main.varSkm <- main.var$u
plot(main.var$km, main.varSv, xlim=c(0,60), ylim=c(0,15), pch=16,col=rgb(0,0,1))
#

abline(v=0, col="gray", lty=2)

abline(h=var(main.xyz$olsr), col=”red", lty=3)

#

# Examine empirical variogram and fit a variogram model by eye.
# (of the flexible Matern class)

#

my.nug <- 2.2

my.sil <- 3.5

my.ran <- 19

my.kap <- 0.5

lines.variomodel(cov.model="matern", cov.pars=c(my.sil,my.ran), ~
nugget=my.nug, kappa=my.kap, max.dist=60, col="black", lty=1)

#

# Write positions and residuals to a CSV file to visualize pattern in a GIS.
#

write.csv(main.xyz, file="mainxyz.csv”, row.names=FALSE)

#

###########################################################

319

###########################################################
second.R

Scott A. Drzyzga
Summer 2006

Purpose: to fit polynomial uplift model via generalized least squares.

Dependencies (packages):
gstat, geoR, and sp.

Dependencies (objects):

distmat: a matrix object that contains distances between pairs of
paleoshoreline data.

my.nug, my.si1, my.ran, and my.kap: parameters of the chosen
variogram model (assuming Matern class).

main.xyz: a data.frame object that contains paleoshoreline position
data and OLS residuals - obtained from first.R script.

main.formu1a: formula object that specifies form of the trend model

##########################################################

Build the spatial covariance matrix.

##4titit1titflt3t1tit4tit4tititit4t4tit4t4t4tfit

main.cov <- cov.spatial(dist.mat, cov.model=c("pure.nugget","matern"),
cov.pars=rbind(C(my.nug,0),c(my.si1,my.ran)), kappa=my.kap)

#

# Alternate covariance matrix when spatial structure is absent.

#

# main.cov <- cov.spatial(dist.mat, cov.mode1="pure.nugget", cov.pars=c(4,0))
#

# Fit model via Generalized Least Squares (GLS).

# Examine model for fitness and assess residuals for warning signs.

#

main.gls <-1m.gls(formula=main.formula, data=main.xyz, W=main.cov, ~
inverse=TRUE)

#

main.xyz$glsr <- main.gls$residuals

summary(main.gls$residuals)

qq.plot(main.xyz$glsr)

#

320

Examine GLS residuals for signs of any remaining spatial structure.
Conduct a variography of GLS residuals.
Explore, visualize, and assess interactively.

##2##:41:

main.grgeo <- as.geodata(main.xyz, coords.col=5:6, data.col=8)
main.gr.var <- variog(main.gr.geo, option="bin", pairs.min=6, ~
breaks=seq(0,60,range))

#

main.gr.varSkm <- main. gr.var$u

write.csv(main.xyz, file="mainxyz.csv", row.names=FALSE)
plot(main.gr.var$km, main. gr.var$v, xlim=c(0,60), ylim=c(0,15), pch=16, ~
col=rgb(0,0,1))

#

abline(v=0, col="gray", lty=2)

abline(h=var(main.xyz$glsr), col="red", lty=3)

# 1ines.variomodel(cov.model="pure.nugget", cov.pars=c(4,0), nugget=0, ~
max.dist=60, col="black", lty=1)

#

lines.variomode1(cov.model="matern", cov.pars=c(my.sil, my.ran), ~
nugget=my.nug, kappa=my.kap, max.dist=60, col="black", lty=1)#

#
###########################################################

321

###########################################################
third.R

Scott A. Drzyzga
Summer 2006

Purpose: Assess prediction model via cross-validated universal kriging.

Dependencies (packages):
gstat, geoR, and sp.

Dependencies (objects):
my.nug, my.sil, my.ran, and my.kap: parameters of the chosen
variogram model (assuming Matern class).
main.xyz: a data.frame object that contains paleoshoreline position
data and OLS residuals — obtained from first.R script.
main.formu1a: formula object that specifies form of the trend
model.

##########################################################

Build prediction model with trend and aspatial variance components only.
Start by establishing a gstat object and the underlying trend component.

##4t3tit1t4tfitit4t4tit4tit3tititititititititfi

main.pnug.gstat <- gstat(id="lake", formula=main.formula, locations=~x+y,
data=main.xyz)

#

# Add aspatial variance component to the gstat object (pure nugget)

#

main.pnug.gstat <- gstat(main.pnug.gstat, id="1ake", ~
model=vgm(psill=my.sil+my.nug, model="Nug", range=0, nugget=0))

#

# Generate residuals via cross-validated universal kriging.
# Explore, visualize, and assess interactively.
#

main.pnug.cvuk <- gstat.cv(main.pnug.gstat)

main.xyzSpnug <- main.pnug.cvukSresidual

qq.plot(main.xyz$pnug)

summary(main.xyz$pnug)

#

# Build another prediction model with spatial trend, spatial covariance, and
# aspatial variance components.

322

# Start by establishing a gstat object and the underlying trend component.
#

main.gstat <- gstat(id="lake", formula=main.formula, locations=~x+y, ~
data=main.xyz)

#

# Specify a variogram model that describes spatial covariance structure.
# Add it to the gstat object.

#

main.vgm <- vgm(psill=my.sil, model="Mat", range=my.ran*10, nugget=my.nug,
~ kappa=my.kap, anis=c(110,0.1))
main.gstat <- gstat(maingstat, id="1ake", model=main.vgm)

Generate residuals via cross-validated universal kriging.
Explore, visualize, and assess interactively.
Write results to a CSV file for import into a GIS.

##1##:41:

main.cvuk <- gstat.cv(maingstat)
main.xyz$cvukr <- main.cvukSresidual
qq.plot(main.xyz$cvukr)

#

write.csv(main.xyz, file="mainxyz.csv", row.names=FALSE)
###########################################################

323

###########################################################
predictWaterplane.R

Scott A. Drzyzga
Summer 2006

Purpose: to generate prediction and uncertainty surfaces for the Main
Algonquin water plane.

This specific script can be modified to predict other water planes given an
appropriate sample of x,y,z data..

Dependencies (packages):
gstat, geoR, and sp.

Dependencies (objects):
main. gstat: a gstat object that specifies the prediction method and
variogram model.
predicthere: a data.frame object with grid cell locations (in local
coordinate system) where predictions should occur.

##########################################################

Load required packages, if not loaded already.
Allocate a large chunk of RAM to the process.

##=fl:##=fl:=¢¢t¢t##ititittitdtitititititittit

library(geoR)

library(gstat)

library(maptools)

memory.limit(1700)

#

# Load file containing coordinates of locations needing predictions
# (in local coordinate system).

#

load("C:/ rdata/ phd/waterplanes/ predicthere")

Surface prediction via universal kriging

11:41:43:

predict <- predict.gstat(maingstat, newdata=main.grd, BLUE=FALSE, nsim=0)
colnames(predict) <- cbind("x","y","pred","kvar")

#

# Scale and translate local coordinates back to MIGEOREF coordinates

324

#
predict$x <- predict$x * 1000 + 532000
predict$y <- predict$y * 1000 + 468000

Reformat data.frame for export to ASCII grid format.
Undocumented quirk:
Setting the na.value to an integer value will create an integer grid.
Setting the na.value to a non-integer value will create a floating
point grid.

itit4t=3t=lt=tt=tt=lt

 

coordinates(predict) <- ~x+y

gridded(predict) <- TRUE

write.asciigrid(predict, "mainPred.asc", attr="pred", na.value=-99.9)
write.asciigrid(predict, "mainKvar.asc", attr="kvar", na.value=-99.9)

 

rm(predict, main.grd)

#

#

# Garbage collection: returns memory to the operating system after a

memory-hogging model run.

41:41:08? 31:41:41:
0

###########################################################

325

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